Question

A current-carrying circular coil of 100 turns and radius 5.0 cm produces a magnetic field of 6.0 × 10⁻⁵ T at its centre. Find the value of the current.

Answer 1

Given:
No. of turns, n = 100
Radius of the loop, r = 5 cm = 0.05 m
Magnetic field intensity, B = 6.0 × 10⁻⁵ T
Now, let the magnitude of current be i.

$$\text{ Using }B=\frac{{\mu }_0\text{ ni}}{2r},\text{ we get }$$
$$6.0\times {10}^{-7}=\frac{4\pi \times {10}^{-7}\times {10}^2\times i}{2\times 0.05}$$
$$\Rightarrow i=\frac{60\times {10}^{-7}}{4\pi \times {10}^{-7}\times {10}^2}$$
$$=4.777\times {10}^{-2}\approx 48$$  mA