Chapter 21, Problem 11P

To determine

Answer to Problem 11P

Induced current direction in the circular loop due to changing current in the wire placed near it.

Solution:

Explanation of Solution

In Figure (a): No induced current.
Figure (b): Induced current flows in clockwise direction
Figure (c): Induced current flows in anti-clockwise direction
Figure (d): Induced current flows in clockwise direction

In figure (a)no induced current flows because the flux linked with the loop due to steady current in wire is not changing.

In figure (b)by right hand rule, the magnetic field of the current in wire acts on the loop in a direction perpendicular to the plane and inwards. By Lenz’s law, the induced current should oppose the decrease in flux that is it should also produce inward flux so the induced current flows in the clockwise direction.

In figure (c)by right hand rule, the magnetic field of the current in wire acts on the loop in a direction perpendicular to the plane and outwards. By Lenz’s law, the induced current should oppose the decrease in flux that is it should also produce outward flux so the induced current flows in the anticlockwise direction.

In figure (d)by right hand rule, the magnetic field of the current in wire acts on the loop in a direction perpendicular to the plane and outwards. By Lenz’s law, the induced current should oppose the increase in flux that is it should also produce inward flux so the induced current flows in the clockwise direction.

Conclusion:

Direction of induced current in a circuit is such that it opposes the cause or the change which produces it.