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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A conducting loop of face-area A and resistance R is placed perpendicular to a magnetic field B. The loop is withdrawn completely from the field.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 Note that it is independent of the shape of the loop as well as the way it is withdrawn.
Solution
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It is given that the loop is withdrawn from the magnetic field.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 \[q = it = \frac{BA}{R}\]
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