# B inside a hollow cylinder

1. Nov 5, 2012

### mateomy

A few of my classmates and I are in a debate about whether or not there would be a magnetic field within a hollow cylinder. The problem has a solid cylinder with current running (throughout the solid) along its axis. Slightly off-center is a hollowed out 'hole' that runs the length of the infinite cylinder. We are arguing over whether or not there is a B-field in there, one side says no and the others are saying yes. We've shown each other our mathematical arguments but the debate proceeds.

Can anyone confirm either in the affirmative or negative?

One side is using the argument of vector potential being present, and the other is using an Amperian loop to show it is zero as no current is enclosed.

2. Nov 6, 2012

### rude man

Think as follows: assume a constant current density thruout the cylinder cross-section. Then add an equal but opposite current density where your offset hole is. Then just add the effects of the two currents as you draw your amperian loops.

Just drawing an amperian loop the way you describe is inadequate. The fact that ∫Bdl = 0 around a loop with no current piercing it does not mean B is zero everywhere around the loop unless there is symmetry which is not the case here.

I have no access to any books right now so can't comment on the relevance of the magnetic potential.

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