Question

An electron moving along the line AB which lies in the same plane as a circular loop of conducting wire as shown in figure. The direction of the induced electric field in the loo will be
A. no current will be induced
B. clockwise
C. anticlockwise
D. the current will change direction as the electron passes by

Answer 1

Hint: Use the concept of Lenz law. First determine the direction of the induced current when the electron is near the circular loop and then determine the direction of the induced emf when the electron is moving away from the circular loop. Check the direction of the induced current for the whole travel of the electron.

Complete step by step answer:
We have given that the electron is moving along the line AB and the line AB lies in the same plane as a circular loop[ of conducting wire.
The diagram for the circular loop and electron moving long line AB is as follows:

The direction of the electric current is opposite to the direction of motion of the electron.
Hence, if the electron moves from point A to B the direction of the current due to the motion of the electron will be in the opposite direction.
When the electron is moving along the line AB, there is a magnetic field produced due to the electron in motion.
As the electron passes through the circular loop, the strength of the magnetic field due to the electron increases. This results in an increase in the flux passing through the circular loop.
We know that the changing flux causes the emf to produce. But this produced emf is in such a direction that it opposes the increase in flux passing through the area of the circular loop.
Thus, the electric current induced in the circular loop will be in an anti-clockwise direction.
But when the electron moves away from the loop, the strength of the magnetic field due to motion of the electron at the circular loop decreases. This causes a decrease in the flux passing through the circular loop.
The induced current in the circular loop opposes the decrease in the flux and this current starts flowing in clockwise direction.
Therefore, the direction of the induced current changes as the electron passes by.

So, the correct answer is “Option D”.

Note:
The students should keep in mind that the direction of the induced current depends on the flux linked with the area of the circular loop. The increase in the strength of the magnetic field increases the flux linked with the loop and the induced current in the loop will be in such a direction that it tries to change the direction of the magnetic field due to current in the line AB.