A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the field. Some how, the radius of the loop starts shrinking at a constant rate of 2 mm/s. Find the induced emf in the loop at an instant when the radius becomes 2 cm solution.

Explanation

Let the radius of the loop be r at time t the magnetic flux linked with the loop at this instant is,
`phi=AB=pir^2B`
The induced emf in the loop at time t,
`|epsilon|=(dphi)/(dt)`
`=d/(dt)[pir^2B]`
`=2pirB(dr)/(dt)`
Here B=0.04 T , r=2 cm
`=2xx10^(-2)` m
`(dr)/(dt)=2 (mm)/s`
`=2xx10^(-3)m/s`
`=2pixx2xx10^(-2)xx0.04xx2xx10^(-3)`
`therefore |epsilon|=0.32pixx10^(-5)V`
`therefore |epsilon|=3.2pixx10^(-6)V=3.2pi muV`