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)I)/(2b)omega cos omegat`
B. `(pia^(2)mu_(0)I)/(2b)omega sin omega^(2)t^(2)`
C. `(pia^(2)mu_(0)I)/(2b)omega sin omegat`
D. `(pia^(2)mu_(0)I)/(2b)omega sin^(2) omega t`

Answer

C

Explanation

We know that, e = NBA `omegasin omegat`
where, N = number of loops = 1
`B=(mu_(0)I)/(2b)N//A-mrArr A= pia^(2)m^(2)`
`therefore" "e=(mu_(0)I)/(2b)(pia^(2))omega sin omegat`
`rArr" "=(pia^(2)mu_(0)I)/(2b).omega sin omega t`