Radius of a conducing wire r and its plane is perpendicular to magnetic field B. If the conductors is stretched and made in shape of square in its plane and in time t, then induced a emf `epsilon` is _____

Options

A. `(piBr^2)/t(1-pi/10)`
B. `(piBr^2)/t(1-pi/8)`
C. `(piBr^2)/t(1-pi/6)`
D. `(piBr^2)/t(1-pi/4)`

Answer

D

Explanation

Length of wire l=`2pir` and area `=pir^2`
The length of side of square made is
`l.=l/4=(2pir)/4=(pir)/2`
Area `A_2=((pir)/2)^2`
`therefore DeltaA=A_1-A_2`
`=pir^2-((pir)/2)^2`
`=pir^2-(pi^2r^2)/4=pir^2(1-pi/4)`
`therefore` Induced emf `|epsilon|=(BDeltaA)/t=(Bpir^2)/t(1-pi/4)`