Applications in Potential Theory and Electromagnetic Theory:
Multiple Choice Questions
1. What is the electric field intensity at a distance r from a point charge Q in free space?
a) E = Q / (4πε r²)₀
b) E = Q / (2πε r²)₀
c) E = Q / (4πε r)₀
d) E = Q / (2πε r)₀
Answer: a) E = Q / (4πε r²)₀
2. In electrostatics, Gauss's law states that the electric flux through a closed surface is
proportional to:
a) The electric field strength
b) The enclosed charge
c) The surface area
d) The permittivity of the medium
Answer: b) The enclosed charge
3. Which of the following is the correct expression for the electric potential due to a point charge
Q at a distance r?
a) V = Q / (4πε r)₀
b) V = Q / (4πε r²)₀
c) V = Q / (2πε r)₀
d) V = Q / (2πε r²)₀
Answer: a) V = Q / (4πε r)₀
4. The divergence of the electric field E in a region with charge density ρ is given by:
a) · E = ρ/ε∇ ₀
b) · E = ε ρ∇ ₀
c) · E = ρ∇
d) · E = 0∇
Answer: a) · E = ρ/ε∇ ₀
5. In magnetostatics, the magnetic field B is related to the magnetic vector potential A by:
a) B = × A∇
b) B = · A∇
c) B = - A∇
d) B = ²A∇
Answer: a) B = × A∇
6. The Biot-Savart law relates:
a) Electric field to charge distribution
b) Magnetic field to current distribution
c) Electric potential to charge distribution
d) Magnetic potential to current distribution
Answer: b) Magnetic field to current distribution
7. Which equation describes Faraday's law of electromagnetic induction?
a) × E = -∂B/∂t∇
b) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
c) · E = ρ/ε∇ ₀
d) · B = 0∇
Answer: a) × E = -∂B/∂t∇
8. The Laplace equation in electrostatics is given by:
a) ²V = 0∇
b) ²V = ρ/ε∇ ₀
c) ²V = -ρ/ε∇ ₀
d) ²V = 1∇
Answer: a) ²V = 0∇
9. In a material with relative permittivity εᵣ, the electric displacement D is related to the electric
field E by:
a) D = εᵣE
b) D = ε E₀
c) D = ε εᵣE₀
d) D = E/εᵣ
Answer: c) D = ε εᵣE₀
10. The magnetic field inside a long solenoid with n turns per unit length and current I is given
by:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
11. Which of Maxwell's equations represents Gauss's law for magnetism?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: c) · B = 0∇
12. The method of images is used to solve problems involving:
a) Magnetic dipoles
b) Electric charges near conducting planes
c) Electromagnetic waves in waveguides
d) Inductance calculations
Answer: b) Electric charges near conducting planes
13. In a material with magnetic permeability μ, the magnetic field strength H is related to the
magnetic flux density B by:
a) B = μH
b) B = H/μ
c) B = μ H₀
d) B = H/μ₀
Answer: a) B = μH
14. The skin depth δ in a conductor with conductivity σ at frequency ω is given by:
a) δ = √(2/ωμσ)
b) δ = √(1/ωμσ)
c) δ = √(ωμσ/2)
d) δ = √(ωμσ)
Answer: a) δ = √(2/ωμσ)
15. The electric field between the plates of a parallel-plate capacitor with plate separation d and
potential difference V is:
a) E = V/d
b) E = Vd
c) E = V²/d
d) E = V/d²
Answer: a) E = V/d
16. In the magnetostatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
17. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
18. The magnetic vector potential A for a long straight wire carrying current I is given by:
a) A = (μ I/2π) ln(r)₀
b) A = (μ I/4π) ln(r)₀
c) A = (μ I/2π) / r₀
d) A = (μ I/4π) / r₀
Answer: a) A = (μ I/2π) ln(r)₀
19. The electric field inside a conducting sphere in electrostatic equilibrium is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
20. The magnetic field at the center of a circular loop of radius R carrying current I is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (2πR)₀
d) B = μ I / (πR)₀
Answer: a) B = μ I / (2R)₀
21. Which of the following is true for the electric potential V in a charge-free region?
a) ²V = ρ/ε∇ ₀
b) ²V = 0∇
c) V = E∇
d) V = -E∇
Answer: b) ²V = 0∇
22. The capacitance of a parallel-plate capacitor with plate area A and separation d is given by:
a) C = ε A/d₀
b) C = ε d/A₀
c) C = ε Ad₀
d) C = ε /Ad₀
Answer: a) C = ε A/d₀
23. In a material with conductivity σ, the current density J is related to the electric field E by:
a) J = σE
b) J = E/σ
c) J = σ/E
d) J = E²σ
Answer: a) J = σE
24. The magnetic field outside a long straight wire carrying current I at a distance r from the wire
is:
a) B = μ I / (2πr)₀
b) B = μ I / (4πr)₀
c) B = μ I / (2r)₀
d) B = μ I / r²₀
Answer: a) B = μ I / (2πr)₀
25. Which of the following is not a solution to Laplace's equation in spherical coordinates?
a) 1/r
b) r
c) r²
d) cos θ
Answer: c) r²
26. The electric field of a point dipole with dipole moment p at large distances r is proportional
to:
a) 1/r²
b) 1/r³
c) 1/r⁴
d) 1/r⁵
Answer: b) 1/r³
27. In the presence of linear dielectric materials, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: a) · E = ρ/ε (becomes · D = ρ)∇ ₀ ∇
28. The electric field of a uniformly charged sphere of radius R and total charge Q at a distance
r > R from its center is:
a) E = Q / (4πε r²)₀
b) E = Q / (4πε R²)₀
c) E = Q / (4πε r)₀
d) E = Q / (4πε R)₀
Answer: a) E = Q / (4πε r²)₀
29. The magnetic field inside a toroidal solenoid with N turns and current I, at a distance r from
the central axis, is given by:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
30. Which of the following is true for a perfect conductor in electrostatic equilibrium?
a) The electric field inside is zero
b) The charge density inside is non-zero
c) The electric potential varies inside
d) The electric field is perpendicular to the surface
Answer: a) The electric field inside is zero
31. The energy stored in a magnetic field B is given by:
a) U = ∫ (B²/2μ ) dV₀
b) U = ∫ (ε E²/2) dV₀
c) U = ∫ (B²/μ ) dV₀
d) U = ∫ (μ B²/2) dV₀
Answer: a) U = ∫ (B²/2μ ) dV₀
32. In the electrostatic approximation, which of Maxwell's equations is neglected?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: b) × E = -∂B/∂t∇
33. The electric field of a uniformly charged infinite line with linear charge density λ at a distance
r is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
34. The magnetic moment m of a current loop with area A and current I is given by:
a) m = IA
b) m = I/A
c) m = I²A
d) m = A/I
Answer: a) m = IA
35. Which of the following is a correct statement of the superposition principle in electrostatics?
a) The total force is the vector sum of individual forces
b) The total potential is the product of individual potentials
c) The total field is the cross product of individual fields
d) The total charge is the sum of individual charges squared
Answer: a) The total force is the vector sum of individual forces
36. The electric field inside a uniformly charged sphere of radius R and total charge Q at a
distance r < R from its center is:
a) E = Q / (4πε R²)₀
b) E = Qr / (4πε R³)₀
c) E = Q / (4πε r²)₀
d) E = Qr² / (4πε R³)₀
Answer: b) E = Qr / (4πε R³)₀
37. The magnetic field of a magnetic dipole with magnetic moment m at large distances r is
proportional to:
a) 1/r²
b) 1/r³
c) 1/r⁴
d) 1/r⁵
Answer: b) 1/r³
38. In a material with relative permeability μᵣ, the magnetic field strength H is related to the
magnetic flux density B by:
a) H = B / (μ μᵣ)₀
b) H = Bμᵣ / μ₀
c) H = B / μ₀
d) H = Bμ / μᵣ₀
Answer: a) H = B / (μ μᵣ)₀
39. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
40. The magnetic flux Φ through a surface S is given by:
a) Φ = ∫ B · dS
b) Φ = ∫ E · dS
c) Φ = B · dl∮
d) Φ = E · dl∮
Answer: a) Φ = ∫ B · dS
41. Which of the following is the correct expression for the Lorentz force on a charge q moving
with velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
Which of the following is the correct expression for the Lorentz force on a charge q moving with
velocity v in electric field E and magnetic field B?
a) F = q(E + v × B)
b) F = q(E - v × B)
c) F = q(v + E × B)
d) F = q(B + v × E)
Answer: a) F = q(E + v × B)
42. The electric field of a uniformly polarized sphere with polarization P at a point outside the
sphere is equivalent to that of:
a) A point charge at the center
b) A dipole at the center
c) A uniformly charged sphere
d) A uniformly charged shell
Answer: b) A dipole at the center
43. In a good conductor, the relaxation time τ is related to the conductivity σ and permittivity ε
by:
a) τ = ε/σ
b) τ = σ/ε
c) τ = σε
d) τ = 1/(σε)
Answer: a) τ = ε/σ
44. The magnetic field inside a long cylindrical conductor carrying a uniformly distributed current
I is proportional to:
a) 1/r
b) r
c) r²
d) Independent of r
Answer: b) r
45. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) E and B are parallel
b) E and B are perpendicular to each other and to the direction of propagation
c) E and B are perpendicular to each other but parallel to the direction of propagation
d) E and B are both parallel to the direction of propagation
Answer: b) E and B are perpendicular to each other and to the direction of propagation
46. The speed of electromagnetic waves in a medium with relative permittivity εᵣ and relative
permeability μᵣ is:
a) c/√(εᵣμᵣ)
b) c√(εᵣμᵣ)
c) c/(εᵣμᵣ)
d) c(εᵣμᵣ)
Answer: a) c/√(εᵣμᵣ)
47. The electric field of a point charge Q in a medium with permittivity ε at a distance r is:
a) E = Q / (4πεr²)
b) E = Q / (4πεr)
c) E = Q / (2πεr²)
d) E = Q / (πεr²)
Answer: a) E = Q / (4πεr²)
48. The mutual inductance M between two coils is defined as:
a) M = Φ /I₁₂ ₁
b) M = I /Φ₁ ₁₂
c) M = Φ I₁₂ ₁
d) M = Φ + I₁₂ ₁
Answer: a) M = Φ /I₁₂ ₁
49. Which of the following is true for the electric field E and magnetic field B of a plane
electromagnetic wave in free space?
a) |E| = c|B|
b) |E| = |B|/c
c) |E| = c²|B|
d) |E| = |B|
Answer: a) |E| = c|B|
50. The magnetic field at the center of a Helmholtz coil pair (two identical coils separated by a
distance equal to their radius R) each carrying current I is:
a) B = (4/5)³/² (μ NI/R)₀
b) B = (8/5)³/² (μ NI/R)₀
c) B = (16/5)³/² (μ NI/R)₀
d) B = (32/5)³/² (μ NI/R)₀
Answer: b) B = (8/5)³/² (μ NI/R)₀
51. The electric field inside a parallel-plate capacitor with surface charge density σ on each
plate is:
a) E = σ/ε₀
b) E = σ/(2ε )₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/ε₀
52. In the magnetoquasistatic approximation, which of Maxwell's equations is modified?
a) · E = ρ/ε∇ ₀
b) × E = -∂B/∂t∇
c) · B = 0∇
d) × B = μ J + μ ε ∂E/∂t∇ ₀ ₀ ₀
Answer: d) × B = μ J + μ ε ∂E/∂t (becomes × B = μ J)∇ ₀ ₀ ₀ ∇ ₀
53. The magnetic field inside a toroid with N turns, current I, and average radius r is:
a) B = μ NI / (2πr)₀
b) B = μ NI / r₀
c) B = μ NI / (2r)₀
d) B = μ NI / (πr)₀
Answer: a) B = μ NI / (2πr)₀
54. The electric field of a uniformly charged infinite cylinder with linear charge density λ at a
distance r from its axis (r > R, where R is the cylinder radius) is:
a) E = λ / (2πε r)₀
b) E = λ / (4πε r)₀
c) E = λ / (πε r²)₀
d) E = λ / (2πε r²)₀
Answer: a) E = λ / (2πε r)₀
55. The magnetic vector potential A for a magnetic dipole with moment m at large distances r is
proportional to:
a) 1/r
b) 1/r²
c) 1/r³
d) 1/r⁴
Answer: a) 1/r
56. In a material with complex permittivity ε = ε' - jε", the loss tangent is defined as:
a) tan δ = ε"/ε'
b) tan δ = ε'/ε"
c) tan δ = ε'ε"
d) tan δ = ε' + ε"
Answer: a) tan δ = ε"/ε'
57. The electric field of a point charge Q in a medium with conductivity σ and permittivity ε at a
distance r, considering the relaxation of charge, is proportional to:
a) e ᵗ/τ / r²⁻
b) e ʳ/τ / r²⁻
c) e ᵗ/τ / r⁻
d) e ʳ/τ / r⁻
Answer: a) e ᵗ/τ / r²⁻
58. The skin depth δ in a good conductor at angular frequency ω is proportional to:
a) ω^(1/2)
b) ω^(-1/2)
c) ω
d) ω^(-1)
Answer: b) ω^(-1/2)
59. The electric field of a uniformly charged ring with total charge Q and radius a at a point on its
axis at a distance z from the center is:
a) E = Qz / [4πε (z² + a²)³/²]₀
b) E = Qa / [4πε (z² + a²)³/²]₀
c) E = Q / [4πε (z² + a²)³/²]₀
d) E = Qz / [4πε (z² + a²)]₀
Answer: a) E = Qz / [4πε (z² + a²)³/²]₀
60. The magnetic field of a uniformly magnetized sphere with magnetization M at a point outside
the sphere is equivalent to that of:
a) A point magnetic charge at the center
b) A magnetic dipole at the center
c) A uniformly magnetized shell
d) A current loop at the equator
Answer: b) A magnetic dipole at the center
61. In a waveguide, the cutoff frequency fc for the TE mode in a rectangular waveguide with ₁₀
width a is:
a) fc = c / (2a)
b) fc = c / a
c) fc = 2c / a
d) fc = c / (4a)
Answer: a) fc = c / (2a)
62. The electric field of a point charge Q near a grounded conducting plane can be calculated
using the method of images. The equivalent system consists of:
a) Two equal charges Q at equal distances on opposite sides of the plane
b) Two opposite charges ±Q at equal distances on opposite sides of the plane
c) A single charge Q and its mirror image -Q on the other side of the plane
d) A single charge Q and a uniform surface charge on the plane
Answer: c) A single charge Q and its mirror image -Q on the other side of the plane
63. The magnetic field at the center of a square loop with side length a carrying current I is:
a) B = (2√2μ I) / (πa)₀
b) B = (4μ I) / (πa)₀
c) B = (2μ I) / (πa)₀
d) B = (√2μ I) / (πa)₀
Answer: a) B = (2√2μ I) / (πa)₀
64. The electric field of a uniformly charged disk with surface charge density σ and radius R at a
point on its axis at a distance z from the center is:
a) E = (σ/2ε ) [1 - z/√(z² + R²)]₀
b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
c) E = (σ/ε ) [1 - z/√(z² + R²)]₀
d) E = (σ/ε ) [1 + z/√(z² + R²)]₀
Answer: b) E = (σ/2ε ) [1 + z/√(z² + R²)]₀
65. The magnetic field inside a long solenoid with n turns per unit length and current I is:
a) B = μ nI₀
b) B = μ I/n₀
c) B = μ n²I₀
d) B = μ I/(2πn)₀
Answer: a) B = μ nI₀
66. The electric field of a point dipole with dipole moment p at a distance r in the direction θ from
the dipole axis is proportional to:
a) (2cos θ r
g + sin θ θg) / r³
b) (cos θ r
g + sin θ θg) / r³
c) (2cos θ r
g - sin θ θg) / r³
d) (cos θ r
g - sin θ θg) / r³
Answer: a) (2cos θ r
g + sin θ θg) / r³
67. The magnetic vector potential A for a long straight wire carrying current I at a distance r from
the wire is:
a) A = (μ I/2π) ln(r) ẑ₀
b) A = (μ I/4π) ln(r) ẑ₀
c) A = (μ I/2π) / r ẑ₀
d) A = (μ I/4π) / r ẑ₀
Answer: a) A = (μ I/2π) ln(r) ẑ₀
68. The electric field inside a uniformly charged spherical shell is:
a) Zero
b) Constant and non-zero
c) Proportional to the radius
d) Inversely proportional to the radius squared
Answer: a) Zero
69. The magnetic field of a current sheet with surface current density K is:
a) B = μ K/2₀
b) B = μ K₀
c) B = K/2ε₀
d) B = K/ε₀
Answer: a) B = μ K/2₀
70. The electric field of a uniformly charged infinite plane with surface charge density σ is:
a) E = σ/(2ε )₀
b) E = σ/ε₀
c) E = 2σ/ε₀
d) E = σ²/ε₀
Answer: a) E = σ/(2ε )₀
71. The magnetic field of a uniformly magnetized sphere with magnetization M at a point inside
the sphere is:
a) B = (2/3)μ M₀
b) B = μ M₀
c) B = (1/3)μ M₀
d) B = (4/3)μ M₀
Answer: a) B = (2/3)μ M₀
72. The electric potential of a conducting sphere of radius R with charge Q is:
a) V = Q / (4πε R) for r ≥ R₀
b) V = Q / (4πε r) for r ≥ R₀
c) V = Q / (4πε R) for all r₀
d) V = Q / (4πε r) for all r₀
Answer: a) V = Q / (4πε R) for r ≥ R₀
73. The magnetic field of a current-carrying wire bent into a semicircle of radius R at the center
of the semicircle is:
a) B = μ I / (2R)₀
b) B = μ I / R₀
c) B = μ I / (4R)₀
d) B = μ I / (πR)₀
Answer: b) B = μ I / R₀
74. The electric field of a point charge Q in a medium with dielectric constant κ at a distance r is:
a) E = Q / (4πε κr²)₀
b) E = κQ / (4πε r²)₀
c) E = Q / (4πε r²κ)₀
d) E = κQ / (4πε r)₀
Answer: a) E = Q / (4πε κr²)₀
75. The magnetic flux through a loop of wire in a changing magnetic field induces an emf given
by:
a) ε = -dΦ/dt
b) ε = dΦ/dt
c) ε = -∫(dΦ/dt)dt
d) ε = ∫(dΦ/dt)dt
Answer: a) ε = -dΦ/dt
76. The electric field inside a uniformly charged solid sphere of radius R and total charge Q at a
distance r < R from its center is:
a) E = Q / (4πε R²)₀
b) E = Qr / (4πε R³)₀
c) E = Q / (4πε r²)₀
d) E = Qr² / (4πε R³)₀
Answer: b) E = Qr / (4πε R³)₀
77. The magnetic field of a long straight wire carrying current I at a distance r from the wire is:
a) B = μ I / (2πr)₀
b) B = μ I / (4πr)₀
c) B = μ I / (2r)₀
d) B = μ I / r²₀
Answer: a) B = μ I / (2πr)₀
78. The electric field of a point dipole with dipole moment p at large distances r is proportional
to:
a) 1/r²
b) 1/r³
c) 1/r⁴
d) 1/r⁵
Answer: b) 1/r³
79. The magnetic fiel
