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7 problems for EM

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1. (20 points) A long rectangular resistor of length L is made from a material with

conductivity s. The ends of the resistor are rectangular with width W and height H.

The potential difference between the rectangular ends is V. The electric field is

constant through the resistor, but its value is not given.

a. What is the current that flows from one end to the other?

b. What is the resistance?

2. (20 points) Two metal spherical shells are separated by a material with

resistivity ?. The inner metal spherical shell has radius M, and the outer metal

spherical shell has radius N. The potential difference between the two shells is V.

a. What is the current that flows from the inner shell to the outer shell?

b. What is the resistance?

3. (40 points) Test the following hypothetical electric fields to determine if they

could be solutions to the wave equation.

a. ? = ?! ? !”# – ?! ? !!”

b. ? = ?! cos(??) + ?! sin(??)

c. ? = ?! sin(?? – ??) – ?! ? !(!!”!!”)

d. ? = ?! ? !(!”!!”) + ?! ? !!(!”!!”)

4. (17.5 points) A steady current ? = ??!/! ? flows down a long cylindrical wire of

radius R. (k is a constant.) Find the magnetic field, both inside and outside the

wire, using Ampères Law.

5. (17.5 points) A slab of current is infinitely long in the y direction. In the z

direction, the slab extends from z = -A to z = +A. The current through the slab is

? = ?? ! ? . Find the magnetic field both inside and outside the slab.

6. (17.5 points) A cylindrical, infinitely long region of space of radius R has a

magnetic field that can be written as ?(?, ?, ?, ?) = ?? ! ? ! ? . What is the electric

field induced inside radius R and outside radius R?

7. (17.5 points) The current to an infinitely long solenoid of radius A is being

decreased so that the current can be written as ? ? = ?? !! ?. The solenoid has n

turns per unit length. What is the electric field induced inside and outside the

solenoid?

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