Question

Figure shows planar loops of different shapes moving out of or into a region of magnetic field which is directed normal to the plane of loops downwards. Determine the direction of induced current in each loop using Lenz’s law.

Answer 1

We know that current is produced when the magnetic flux in a closed loop is changed and current is produced in such a way that this current opposes the magnetic flux. So, if we simply find the direction of the increase or decrease of the magnetic flux the current moves just to oppose this flux.

Complete step by step answer:
Lenz’s law: In a closed loop if the magnetic flux changes an induced electric current flow in a direction such that the current opposes the change that induced it.
Figure (i)

The loop (a b c d) is entering the magnetic field, so the flux linked with them increases as the area of the loop that comes under the influence of the magnetic field increases. Thus, the direction of the induced currents in this coil will be in such a way that it opposes the increase of magnetic flux; hence, the magnetic field due to current-induced current will be upward (against the direction of increasing magnetic flux). So, the currents induced will be in an anticlockwise direction.

Figure (ii)

The loop (a b c) is coming out from the magnetic field, therefore magnetic flux linked with these loops decreases as the area of the loop that comes under the influence of the magnetic field decreases. Thus, the direction of the induced currents in this coil will be in such a way that it opposes the decrease of magnetic flux; hence, the magnetic field due to current-induced current will be downward (against the direction of decreasing magnetic flux). So, the currents induced will be in clockwise direction.

Figure (iii)

The circular loop is entering the magnetic field, so the flux linked with them increases as the area of the loop that comes under the influence of the magnetic field increases. Thus, the direction of the induced currents in this coil will be in such a way that it opposes the increase of magnetic flux; hence, the magnetic field due to current-induced current will be upward (against the direction of increasing magnetic flux). So, the currents induced will be in an anticlockwise direction.

Figure (iv)

The loop is coming out from the magnetic field, therefore magnetic flux linked with these loops decreases as the area of the loop that comes under the influence of the magnetic field decreases. Thus, the direction of the induced currents in this coil will be in such a way that it opposes the decrease of magnetic flux; hence, the magnetic field due to current-induced current will be downward (against the direction of decreasing magnetic flux). So, the currents induced will be in clockwise direction.

Finally in loop (i) and loop (iii) the currents induced will flow anticlockwise and the loop (ii) and loop (iv) the current induced will flow clockwise.

Note: Be very careful with the direction when applying Lenz's law. Sometimes in some tricky questions the loop remains same and in a stationary condition, but either the area of the loop or the magnetic field that passes through the loop changes this also creates an induced current, and the direction of this induced current produced can also be determined by using simply by using Lenz’s law (by finding out the direction of change in magnetic flux).