(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A long straight cylindrical shell has an inner radius Ri and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r < Ri). The magnetic field is zero everywhere outside the shell (r > Ro). We conclude that the wire:

- may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell
- 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
- does not carry any current
- is on the cylinder axis and carries current i in the same direction as the current in the shell
- is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell

(each option is a radio button)

2. Relevant equations

[tex]\oint \vec{B} \cdot d\vec{s} = \mu_0 i_{enc}[/tex]

3. The attempt at a solution

Total enclosed current is the algebraic sum of each portion of enclosed current. Therefore, to get [tex]\oint B \cdot ds = 0[/tex] any current within the amperian loop (in this case, loop is the outer surface of the shell) must be compensated for by current flowing in the opposite direction. I don't see why the relative positions of the current-carrying bodies are of any relevence. So I said that the answer was 3. But the book says the answer is 5: the wire must be on the cylinder's axis. Can I have a pointer as to why the position of the wire matters, as long as the wire is within the amperian loop?

edit: stupid mistake. I said that the answer was2not 3.

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# Homework Help: Ampere's Law: Conceptual

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