A very small circular loop of radius a is initially (at t = 0) coplanar and concentric with a much larger fixed circular loop of radius b. A constant current I flows in the larger loop. The smaller loop is rotated with a constant angular speed `omega` about the common diameter. The emf induced in the smaller loop as a function of time t is

Options

A. `(pia^(2)mu_(0)l)/(2b)omegacos omegat`
B. `(pia^(2)mu_(0)l)/(2b)omegasinomega^(2)t^(2)`
C. `(pia^(2)mu_(0)l)/(2b)omegasin omegat`
D. `(pia^(2)mu_(0)l)/(2b)omega sin^(2) omega t`

Answer

C

Explanation

We know that e=NBA `omega sini omegat`
where, `N=`Number of loops=1
`B=(mu_(0)l)/(2b)N//A^(-1)m^(-1)impliesA=pia^(2)m^(2)`
`therefore e=(mu_(0)l)/(2b)(pia^(2))omega sin omega t`
`implies e=(pia^(2)mu_(0)l)/(2b)*omegasin omegat`