Question

A magnetic field is produced along the axis of a current-carrying loop. The direction and magnitude of the magnetic field at the center of the loop can be determined using the Biot-Savart law. What will be the direction of the magnetic field along the axis of the current loop? The magnetic field produced along the axis of a circular current loop is given by the equation: \[ B = \frac{{\mu_0 I R^2}}{{2 (R^2 + x^2)^{3/2}}} \]
where:
\( B \) is the magnetic field,
\( \mu_0 \) is the permeability of free space,
\( I \) is the current,
\( R \) is the radius of the loop,
\( x \) is the distance from the center of the loop along the axis.

• A. Into the plane of the loop
• B. Out of the plane of the loop
• C. Parallel to the loop
• D. Zero

Hint:

For a circular current loop, the magnetic field along the axis can be calculated using the Biot-Savart law, and its direction is determined by the right-hand rule.

Answer 1

The Correct Option is B

For a circular current loop, the magnetic field at the center of the loop is directed along the axis of the loop. The direction of the magnetic field can be determined using the right-hand rule. According to the right-hand rule, if you curl the fingers of your right hand in the direction of the current flow in the loop, the thumb will point in the direction of the magnetic field. For a current flowing in a clockwise direction, the magnetic field will point out of the plane of the loop. Conversely, if the current flows counterclockwise, the magnetic field will point into the plane of the loop. Thus, the correct answer is Option (B): Out of the plane of the loop.