A very small circular loop of radius a is initially coplanar & concentric with a much larger circular loop of radius b `(gtgta)`. A constant current is passed in the large loop which is kept fixed in space & the small loop is rotated with angular velocity omega about a diameter. The resistance of the small loop is R & its self inductance is negligible. The current in the larger loop is clockwise.

Find the current in the small loop as a function of time.

Options

A. `(pia^(2)mu_(0)Iomegasinomegat)/(2bR)`
B. `(pia^(2)mu_(0)Iomegacosomegat)/(2bR)`
C. `(pib^(2)mu_(0)Iomegasinomegat)/(2aR)`
D. `(pib^(2)mu_(0)Iomegacosomegat)/(2aR)`

Answer

A

Explanation

`phi=(mu_(0)I)/(2b)xxpia^(2)cosomegat`
`i=1/R (dphi)/(dt)=r/R=(mu_(0)Ipia^(2)omegasinomegat)/(2bR)`