Question

A conducting loop of face-area A and resistance R is placed perpendicular to a magnetic field B. The loop is withdrawn completely from the field. Find the charge which flows through any cross-section of the wire in the process. Note that it is independent of the shape of the loop as well as the way it is withdrawn.

Answer 1

The magnetic flux through the coil is given by

ϕ = B.A = BA cos 0° = BA

It is given that the loop is withdrawn from the magnetic field.

∴ Final flux = 0

The average induced emf is given by

\[e = - \frac{∆ \phi}{∆ t} = \frac{BA - 0}{t} = \frac{BA}{t}\]

The current in the loop is given by

\[i = \frac{e}{R} = \frac{BA}{tR}\]

The charge flowing through the area of the cross section of the wire is given by \[q = it = \frac{BA}{R}\]