# Metal ring in magnetic field

1. Dec 14, 2011

### beyondlight

1. The problem statement, all variables and given/known data

A metal ring of radius a is located in a region with the homogenous magnetic flux density:

$\hat{B} =\hat{z}B_0 cos(\omega t)$

The metal ring coincides with the plane z=0. The frequency w is very low.

Use Faraday´s Law to determine the electric field where the metal ring is located

2. Relevant equations

$\nabla \times E= -\frac{dB}{dt}$

3. The attempt at a solution

Cylindrical coordinates.

The Electric field is directed in the $\varphi$ direction around the ring.

Rotation of E then becomes:

$-\frac{dE_{\varphi}}{dz}\hat{r} + \frac{1}{r} \frac{d(rE_{\varphi})}{dr}\hat{z}$ = $\hat{z}B_0 \omega sin(\omega t)$

Is this a correct beginning, and how do i proceed from this point?

2. Dec 14, 2011

### rude man

It's admirable to start from the Maxwell relations explicitly. Most people probably would not.

hint: what is Faraday's law?
hint: what relates emf and electric field?

I'm actually looking at your approach, it should of course yield the same result, will be either fun or frustration for me.