- #1

Physgeek64

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## Homework Statement

A thin conducting disc has radius a thickness b and electrical resistivity ρ. It is

placed in a uniform time-dependent magnetic induction ##B = B_0 sin ωt## directed parallel

to the axis of the disc. Assuming that ρ is large, find E at a distance r < a from the axis

of the disc, in the plane of the disc, and obtain an expression for the induced current density as a function of r

## Homework Equations

Maxwells equations

## The Attempt at a Solution

So there are two ways I can think of doing this question. One is to consider the emf induced in the disk using Faradays law ##emf= -{d\phi}/{dt}## and then calculate the associated current using the resistivity, followed by calculating the associated magnetic field. From this I can then calculate the electric field which is produced as a result of this current using ##integral E.ds= -integral {dB}/{dt} .ds## this can then be subtracted from the initial magnetic field to give the resulting.

However, since the resistivity is large, I'm going to assume that this current is essentially negligible. So can I just skip to the point where I can calculate E using ##\integral E.ds= -\integral {dB}/{dt} ds##? My only concern with this, is this electric field is the same regardless of whether the disk is there or not.

Either way, once I have the electric field I can easily calculate the current density. I just can decide which of these methods is more appropriate..

Many thanks

Edit: Really sorry- Don't know how to get the integral sign, nor can I remember where to find how to do it. If you can help me with either of these, that would be much appreciated! :)