Question

A long straight cylindrical shell has an inner radius R_i and an outer radius R_0. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r < R_i).The magnetic field is zero everywhere outside the shell (r > R_0). We conclude that the wire:
a. is on the cylinder axis and carries current i in the same direction as the current in the shell
b. may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell
c. may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell
d. is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell
e. does not carry any current

Answer 1

Answer:

Correct answer is option D

- Wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell

Explanation:

- It cannot be Option E, because the magnetic field outside the wire would not be 0 due to the current carried by the conductor

-Also, the parallel wire cannot carry current in the same direction because, that would amplify the magnetic field created by the outer cylinder (since B is dir. proportional to the current) -and now, that leaves only option C and D. If, it is Option C, then that means one side of the cylinder would be more closer to the parallel wire than the other, so there would be different B fields on the two opposite sides of the cylinder. So, that means the answer is option D.