Question

A very small circular loop of area `5xxI0^(-4)m^(2)` , resistance `2Omega` and negligible inductance is initially coplanar and concentric with a much larger fixed circular loop of radius `0.Im` . A constant current of `IA` is passed in the bigger loop and the smaller loop is rotated with angular velocity `omegarad//sec` about a diameter. Calculate (a) the flux limked with the smaller loop, (b) indced emf (c) induced current in the smaller loop, as a function of time.

Answer 1

Magnetic field due to large loop at centre
`B=(mu_(0)i_(0))/(2a)` (assumed uniform in smaller loop)
Let at any time `t` , normal to small loop makes angle `theta(=omegat)` with magnetic field
(a) Flux throuth smaller loop
`phi=BAcostheta`
`phi=(mu_(0)i_(0))/(2a)Acosomegat`
(b) `e=-(dphi)/(dt)=(mu_(0)i_(0)Aomega)/(2a)sinomegat`
(c) `I=(e)/(R)=(mu_(0)i_(0)Aomega)/(2aR)sinomegat`