# 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