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  1.  (40 points)  A 1.0 m section of an aluminum wire with 2.0 mm diameter carries 1.0 Ampere of electric current in a circuit and has an DC electrical resistance of 0.00845 Ω. The wire is along the x-axis, y=0 and z=0.

 

  1. What is the number of aluminum atoms in 1.0 m of this wire?
  2. What is the electrical conductivity of this Aluminum wire?
  3. Calculate the number of conduction electrons in this 1.0 m of wire.
  4. Calculate the potential difference across this 1.0 m aluminum wire.
  5. Calculate the power dissipation on this 1.0 m wire.
  6. Calculate the electric current density vector, J,  in this wire.
  7. Calculate the average electric field in this wire.
  8. Calculate the Al+3 atom density in this wire.
  9. What is the “+” charge density?
  10. Calculate the conduction electron density in this wire.
  11. What is the net electric charge density on this wire?
  12. Calculate the average speed of electrons in this wire.
  13. A test charge electron coming out of a 1000 V electron gun is travelling along x-axis at y= 0.20 m, z= 0. What is the speed of this electron if the process taking place in vacuum?
  14. What is the velocity vector, v,  of this test electron at that moment where travelling along x-axis?
  15. What is the “+” charge density observed from the inertial frame of moving along x-axis with the same speed as test electron?
  16. What is the speed of conduction electrons in wire observed from the inertial frame of moving along x-axis with the same speed as test electron?
  17. What is the “-” conduction electron charge density observed from the inertial frame of moving along x-axis with the same speed as test electron?
  18. What is the net charge density observed from the inertial frame of moving along x-axis with the same speed as test electron?
  19. What is the force vector on this test electron at that moment?

 

  1. (30) points) A small 1.0 mm water droplet charged with a charge of 2.0x10-6 Coulomb is hanging (x=0, y=0, z=5 cm) over a very large electrically charged metal plane placed on xy plane at z=0.

 

  1. What is the electrical surface charge density of this metal plate?
  2. What is the electrical potential value at the point of this charge?
  3. Determine the electric field vector function at z>0 space ( exclude inside the droplet)

 

  1. (30 points) A vector function given as :     E = (2xy2+ z3, 2x2y, 3xz2)  with a constant to adjust units.

 

  1. Is this a valid function representing static electric field? Show it why or why not ?
  2. Find charge density function ?
  3. Find the associated potential function φ(x, y, z).
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