Question

A circular coil of wire is made up of 200 turns, each of radius 10 cm. If a current of 0.5A passes through it, what will be the magnetic field at the centre of the coil?

Hint:

The magnetic field at the center of a circular coil is directly proportional to the number of turns and the current, and inversely proportional to the radius of the coil.

Answer 1

The magnetic field at the center of a circular coil is given by the formula: \[ B = \frac{\mu_0 N I}{2R} \] where \( N = 200 \) is the number of turns, \( I = 0.5 \, {A} \) is the current, \( R = 10 \, {cm} = 0.1 \, {m} \) is the radius, and \( \mu_0 = 4\pi \times 10^{-7} \, {T m/A} \) is the permeability of free space. Substituting the known values: \[ B = \frac{4\pi \times 10^{-7} \times 200 \times 0.5}{2 \times 0.1} = 6.28 \times 10^{-5} \, {T} \]