Question

The magnitude of the magnetic field due to a circular coil of radius R carrying a current I at its centre is

• A. \( \frac{\mu_0 I}{2R} \)
• B. \( \frac{\mu_0 I}{4\pi R} \)
• C. \( \frac{\mu_0 I}{R} \)
• D. \( \frac{\mu_0 I}{2\pi R} \)

Hint:

For a circular coil, the magnetic field at the centre is proportional to the current and inversely proportional to the radius.

Answer 1

The Correct Option is D

The magnetic field at the centre of a circular coil of radius \( R \) carrying a current \( I \) is given by Ampere's Law: \[ B = \frac{\mu_0 I}{2 \pi R} \] where \( \mu_0 \) is the permeability of free space.
Thus, the magnetic field at the centre of the coil is \( \frac{\mu_0 I}{2 \pi R} \).