A Multiple Choice Question on Lenz’s Law

Two plane coils A and B are arranged coaxially as shown. Using an external battery, an increasing or decreasing clockwise current (as judged by viewing along the axis in the direction marked by the arrow) can be made to flow through coil A. The directions of the induced current through coil B when the current in coil A is (i) increased and (ii) decreased are

(a) clockwise in cases (i) and (ii)

(b) anticlockwise in cases (i) and (ii)

(c) anticlockwise in case (i) and clockwise in case (ii)

(d) clockwise in case (i) and anticlockwise in case (ii)

(e) unpredictable

This is a question based on Lenz’s law in electromagnetic induction, according to which the induced current has to oppose the magnetic flux change which produces the induced current.

When the clockwise current in coil A increases as in case (i), there is an increasing magnetic flux through coil B. The direction of the magnetic field lines (due to the current in coil A) through coil B is along the direction of view marked by the arrow. The induced current in coil B should therefore produce a magnetic field in the opposite direction. Evidently, this will be the case if the sense of induced current in coil B is anticlockwise.

When the current in coil A is decreasing as in case (ii), the flux through coil B is decresing. The direction of the magnetic field lines (due to the current in coil A) is same as in case (i). But the induced current in coil B has to oppose the decrease of the flux. This can be done by producing a magnetic field in the same direction as that produced by coil A. Evidently, the sense of the induced current through coil B must be clockwise for this. So, the correct option is (c).

[Instead of the above lengthy argument, you can have a relatively shorter argument like this:

Coil A has to move away from coil B when the flux linked with coil B increases because of the increasing current in coil A. The required repulsive force between the coils can be produced only if they carry unlike currents. So, the induced current in B in case (i) is anticlockwise. In case (ii) the decrement in the flux linked with coil B can be opposed if coil B moves towards coil A. The attractive force required for this can be produced if the coils carry like currents (currents in the same direction). So, the induced current in B is clockwise in case (ii)].