Question

A rectangular loop of sides \(l\) and \(b\) and resistance \(R\) is kept in a region in which the magnetic field varies as \[ B=B_0\sin\omega t. \] (i) Derive expression for the emf induced in the loop. (ii) Find the effective value of current that flows in the loop.

Hint:

For a loop placed in a magnetic field varying as \[ B=B_0\sin\omega t, \] first calculate the magnetic flux using \[ \Phi_B=BA. \] Then apply Faraday's law \[ e=-\frac{d\Phi_B}{dt}. \] For a sinusoidal current, \[ I_{\text{rms}}=\frac{I_0}{\sqrt{2}}. \] Remember that the peak induced emf is \[ e_0=B_0A\omega. \]

Answer 1