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Re: [Phys-l] Magnetic field from a current loop -- cylindrical coordinates



On 04/10/2012 05:00 AM, Peter Schoch wrote:
My tired, allergy impaired brain needs a bit of help. Last week I did the example problem for a loop of current, in the x-y plane, and finding the magnetic field on the z axis a height P above the loop. I did it in the traditional admixture of cartesian and polar coordinates to get:

dB = mu0 I [ az (cos(theta) xhat + sin(theta) yhat) + a2 zhat] d(theta)/4*pi*R3

If I integrate that from 0 to 2*pi the x and y terms drop out and I get the expected result.

Now, one of my students reworked the problem in cylindrical coordinates and (as far as I can tell) correctly gets:

dB = mu0 I [a z d(theta) rhat + a2 d(theta) zhat] / 4*pi*R3

If I integrate that from 0 to 2*pi I get the correct z term but the rhat term does not go to zero.

Remember that rhat is a function of theta
(unlike xhat, yhat, and zhat which are independent of theta).

Be sure to take that into account when doing the integral over theta.

I'm fairly certain it has to do with the limits of integration, but
can't for the life of me figure out what they are.

The integration runs from 0 to 2pi.
I doubt that is causing any trouble.
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