Induced EMF Problem: Calculate Magnetic Flux & Initial EMF

[carus88]

An elastic conducting material is stretched into a horizontal circular loop of radius 20 cm and placed in a magnetic field of strength 0.5 T, directed vertically downwards.

a. What is the magnetic flux through the loop?

b. When released, the radius of the loop decreases at an initial rate of 50 cm/s; what is the initial emf induced in the loop?

a. i used magnetic flux= BxS and got 0.0628Wb

b. i tried using emf = magneticflux / dt

an used 0.5m/s as dt an the answer for mag flux an got an emf of 0.1256V

part a. is ryt but part b is wrong on the answers

CAN SOMEONE PLEASE TELL ME WHERE IM GOIN WRONG?

THANK YOU FOR YOUR TIME.

 

[Doc Al]

The EMF equals the rate of change of the flux. 0.5 m/s is the rate of change of the radius. (Figure out the rate of change of the area of the circle.)

 

[carus88]

so pi x 0.5^2 ?

 

[Doc Al]

so pi x 0.5^2 ?

The flux is BA = B\pi r^2. You need to find the rate of change of the flux: d(BA)/dt = d(B\pi r^2)/dt. Hint: Use the chain rule.