Question

An electron moven along the line $AB$, which lies in the same plane as a circular loop of conducting wire as shown in the diagram. What will be the direction of current induced if any, in the loop?

• A. No current will be induced
• B. Clockwise
• C. Anticlockwise
• D. The current will reverse its direction as the electron goes past the loop.

Answer 1

The correct option is D The current will reverse its direction as the electron goes past the loop.

As Electron passes along straight line $AB$, its flow is not continous, hence instead of a current carrying wire it will behave like a small current element.
$\Rightarrow$direction of small current $dI$ is from $B\to A$, the magnetic field at centre of loop $\left(B\right)$ due to current element will be perpendicularly inwards to the plane.
$\because B\propto \frac{1}{r^2}$, from biot-savart law.
$\Rightarrow$As electron approaches loop, $(A\to O)$, $r\downarrow$ and the $B$ at centre of loop $\uparrow$, hence current induced in ANTICLOCKWISE direction to oppose it.

Similarly,
$\Rightarrow$As electron goes past the loop, $(O\to B)$, $r\uparrow$ and the $B$ at centre of loop $\downarrow$, hence current induced in CLOCKWISE direction to oppose it.