Question

A small coil, having n turns each of (everage) radius r, is held normal to the magnetic field liens in the region between the (flat) pole pieces of a horse shoe magnet. The terminals ofthe coil are connected to a special galvanometer that can measure the total charge fleming in the circuit. The coil is taken out of the field region in a (small) time Δt and it is observed that a charge Q flows through the coil-galvanometer circuit. The graph that best shows the dependence of the charge flowing (Q) on the time of withdrawl (Δt) of the coil (from the region of the magnetic field), is the graph labelled as graph.

(1) K

(2) L

(3) M

(4) N

Answer 1

(1) K

Let B be the strength of the magnetic field between the poles of the horse shoes magnet. The magnetic flux, linked with the small coil, when it is present in the field region, is

ϕ = (Bπr²)n

The linked magnetic flux becomes zero when it is withdrawn from the field. The instantaneous induced emf, would be

ε = -dϕ/dt

The instantaneous induced current (k) is ε/R where R is the resistance of the coil-galvanometer circuit. The total charge flowing is given by

Q, therefore, does not depend on Δt . This is shown in graph K.