Question

What is Biot-Savart law? Obtain the formula and direction for the intensity of the magnetic field on the axis of an anti-clockwise current-carrying loop with its help.

Hint:

Use Biot-Savart law for problems involving magnetic fields due to current elements or loops.

Answer 1

The Biot-Savart law states that the magnetic field \( dB \) due to a small current element \( Idl \) at a point is given by: \[ dB = \frac{\mu_0}{4 \pi} \frac{I \, dl \, \sin \theta}{r^2}. \] For a circular current loop, the magnetic field on its axis is: \[ B = \frac{\mu_0 I R^2}{2 (R^2 + x^2)^{3/2}}, \] where \( R \) is the radius of the loop, \( x \) is the distance from the center, and \( I \) is the current. The direction of the magnetic field follows the right-hand thumb rule.