Answer to Question #344775 in Electricity and Magnetism for Sophie

Question

A circular loop of wire of radius 0.25 cm is expected to an external magnetic field that is perpendicular to the plane of the loop. For a time, the magnetic field decreases at a rate of 0.0035 T/s. What is the magnitude of the induced electromagnetic force in the loop?

Correct the given Solution:

Solution:

F= SB cos α,

S =πr²,  α= 0°

F= SB cos α

 or F=πr² B

F = (3.14) (0.25) ²  (0.0035)

F= 0.000686875

Or

F= 6.9 x 10^-8 N

Answer 1

$${\cal E}=-\frac{\Delta \Phi}{\Delta t}=-S\frac{\Delta B}{\Delta t}=-\pi r^2\frac{\Delta B}{\Delta t}$$

$${\cal E}=-3.14*(0.25*10^{-2})^2*(-0.0035)\\ =6.9*10^{-8}\:\rm V$$