Question

A wire of irregular shape in figure (a) and a circular loop of wire in figure (b) are placed in different uniform magnetic fields as shown in the figures below. In figure (a), the magnetic field is perpendicular into the plane. In figure (b), the magnetic field is perpendicular out of the plane.

The wire in figure (a) is turning into a circular loop and that in figure (b) into a narrow straight wire. The direction of induced current will be _____.
Fill in the blank with the correct answer from the options given below

• A. clockwise in both (a) and (b)
• B. anticlockwise in both (a) and (b)
• C. clockwise in (a) and anticlockwise in (b)
• D. anticlockwise in (a) and clockwise in (b)

Answer 1

The Correct Option is C

To determine the direction of the induced current, we can apply Lenz's law, which states that the direction of the induced current will be such that it opposes the change in magnetic flux. Let's analyze each scenario separately: 

1. Figure (a): The original configuration is a wire of irregular shape, which is being transformed into a circular loop. The magnetic field is directed perpendicular into the plane. As the irregular wire turns into a circular loop, the area enclosed by the loop increases. Consequently, the magnetic flux through the loop increases because the magnetic field is constant and perpendicular to the loop. To oppose this increase in flux, the induced current will produce a magnetic field out of the plane. Using the right-hand rule, a magnetic field out of the plane corresponds to a clockwise current.
2. Figure (b): The wire initially forms a circular loop and is transformed into a narrow straight wire. The magnetic field in this case is perpendicular out of the plane. As the loop turns into a straight wire, the area enclosed by the loop decreases, which effectively reduces the magnetic flux through the enclosed area. To counteract this decrease in flux, the induced current must generate a magnetic field into the plane. Again, using the right-hand rule, a magnetic field into the plane corresponds to an anticlockwise current.

Therefore, the direction of the induced currents is clockwise in (a) and anticlockwise in (b).