Homework Help: Magnitude of electric field in an area of changing magnetic field

1. Feb 23, 2012

arnab321

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

A cylinder of radius R has a uniform, time varying mag. field B, (dB/dt < 0).
magnitude of electric field at a point P at a distance r (<R) is:

a) decreasing with r
b) increrasing with r
c) not varying with r
d) varying as r^-2

2. Relevant equations

3. The attempt at a solution

i think that electric field should be independent of r, as the field is uniform and doesnt vary with r, and the point is inside the cylinder.

2. Feb 23, 2012

kushan

hey arnab electric field is E=-d(phi)/dt
and phi depend on the area , and area depends on the radius :D

3. Feb 23, 2012

arnab321

i think thats the Emf and not the electric field. anyways, option d is wrong (anyways, ur explaination wasnt even giving option d)

4. Feb 23, 2012

kushan

due Emf and Eds have a relation ?

5. Feb 23, 2012

kushan

sorry that was a typo

6. Feb 24, 2012

arnab321

electric field is (potential) x (dist.) but in this case whats the distance? why does it have to be the distance from centre?

7. Feb 24, 2012

kushan

refer NCERT man its all given there

8. Feb 24, 2012

ehild

The line integral of E around a closed curve is equal to the negative time derivative of the integral of B for the enclosed area.

$$\int{E_s ds}=-\int \frac{\partial B}{\partial t}dA$$

The magnetic field is constant inside the cylinder, so the magnitude of the electric field is constant along a concentric circle by symmetry. Both E and B can be factored out from the integrals...

ehild

Last edited: Feb 24, 2012