E&M
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sample_exam.docEquations and Constants
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1. Three charges lie on the x-axis as shown. q1 = -3.0 x 10-6 C located at the origin, q2 = +4.5 x 10-6 C at x2 = 0.090 m, and q3 = +2.5 x 10-6 C at x3 = 0.03 m.
a. Calculate the magnitude of the total electric force on q3 due to the other two charges.
b. What is the direction of the total electric force on q3?
c. Calculate the magnitude of the electric field at the location x = 0.10 m.
d. What is the direction of the electric field at the location x = 0.10 m?
2. Three charges lie on the x-axis as shown. q1 = -3.0 x 10-6 C located at the origin, q2 = +4.5 x 10-6 C at x2 = 0.090 m, and q3 = +2.5 x 10-6 C at x3 = 0.03 m.
a. How much work is required to assemble the system? (Hint: what is the total potential energy of the system?)
b. What is the total electrical potential at the location x2 = 0.090 m?
c. If q1 and q3 are held at rest and q2 is released from rest, what will be the kinetic energy of q2 when it is infinitely far away?
3. Consider the circuit. ε1 = 15 V, ε2 = 12 V, R1 = 8.0 Ω, R2 = 12 Ω, R3 = 12 Ω.
a. Write the equation from the junction rule at junction A.
b. Write the equation from the loop rule for the clockwise loop A to B to C to D and back to A.
c. Write the equation from the loop rule for the clockwise loop A to D to E to F and back to A.
d. What is the potential difference from point B to point E?
e. [Bonus] Find the current I1.
f. [Bonus] Find the current I2.
g. [Bonus] Find the current I3.
4. Consider the figure below.
a. Find the equivalent resistance between points A and B. (Hint: Reduce the circuit to a single resistor, but do it in three steps).
b. If points A and B are connected to the terminals of a 12-V battery, what is the magnitude of the current through the battery?
5. The circuit below has two capacitors, three resistors, a battery and two switches. The switches, S1 and S2, have been open for a long time and the capacitors are uncharged. At time t = 0 both switches are closed. 1 μF = 10-6 F.
a. Immediately after both switches are closed, what is the current I2?
b. After the switches have been closed for a very long time, what is the current I1?
c. After the switches have been closed for a very long time, what is the total energy, U, stored in the capacitors C1 and C2?
d. After the switches have been closed for a very long time, at time T both switches are opened. Explain what happens next.
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