A conducting loop of face-area A and resistance R is placed perpendicular to a magnetic field B. The loop is withdrawn completely from the field.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 Note that it is independent of the shape of the loop as well as the way it is withdrawn.

Question

Philoid · Accepted Answer

Given:

Face area of loop =A

Resistance of loop=R

Magnetic field intensity =B

Magnetic flux(ϕ) through the loop is given by the formula

Where B=magnetic field intensity

A=area of cross section

θ =angle between area vector and magnetic field

initially loop is perpendicular to the applied magnetic field hence initial flux is

Finally, when the loop is withdrawn from the field flux is given by

Now,

Average induced emf in time interval Δt is given by

…(i)

Where

are flux across the cross section at time intervals respectively

Using eqn.(i) we get

Current flowing in the loop is calculated by using formula

Hence the charge (Q) flowing through the loop is

Therefore, charge flowing through any cross-section of the wire is BA/R