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

The problem is to find the magnetic field within a rotating cylinder (infinitely long) that has on its surface a given surface charge density p. I made a picture of the problem to illustrate this. The only hint given: "the magnetic field outside the cylinder is zero.

2. Relevant equations

Sorry, I cannot use Latex, but:

integral(B,ds) = u0*integral(J,da) where

B is the magnetic field, ds the vector line element, J the current density, da the vector area element.

3. The attempt at a solution

Well, to be cleary, I can solve this problem, but I do not understand a very basic thing.

First I argued by symmetry, that the magnetic field can only be in direction of the angular frequency vector w. Then I took a curve c, illustrated in my picture and now I want to apply the integral law I have written above to this curve c.

I know the left hand side of the integral, which is simply (given that the curve has lengt L):

B*L,

Now I want to calculate the right hand side. Doing so, I first need J. logically:

|J|=(p/(2*pi*R))*(w*R) where (w*R) = v is simply the velocity.

Up to here all is quite easy, but now I have some questions:

i) Is it correct, that the J vector is the tangential vector to the outer surface of the cylinder perpendicular to the angular frequency vector w?

ii) The integral law states that I have to integrate J over the area enclosed by the curve c. But this doesn't seems to be correct. I mean, the area within the cylinder and enclosed by the curve c would then be (R-r1)*L and outside undefined. So over which area do I have to integrate and WHY?

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# Magnetic field of rotating cylinder

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