Question

A very small circular loop of area A and the resistance R and negligible inductance is initially coplanar and concentric with a much larger fixed loop of radius x. A constant current i is passed in the bigger loop and the smaller loop is rotated with constant angular velocity ω about a diameter then induced current in the smaller loop as a function of time will be

• A. $\frac{\mu_{0}iA}{2xR}\sin\omega t$
• B. $\frac{\mu_{0}iA\omega}{2xR}\sin\omega t$
• C. $\frac{\mu_{0}iA\omega}{2xR}\sin 2\omega t$
• D. 0

Answer 1

Answer: (B)

$\frac{\mu_{0}iA\omega}{2xR}\sin\omega t$

Answer 2

At any instant t flux linked with smaller loop $\varphi = BA\cos wt$ where B = magnetic field produced by larger loop at it’s centre $= \frac{\mu_{0}i}{2x}$. So $\varphi = \frac{\mu_{0}iA}{2x}\cos\omega t$

; $e = - \frac{d ⥂ \varphi}{dt} = \frac{\mu_{0}i}{2x}\omega A\sin\omega t$ ⇒ $i = \frac{e}{R} = \frac{\mu_{0}i\omega A}{2xR}\sin\omega t$.