Question

A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is ______. [µ₀ = 12.56 × 10^-7 SI Unit]

विकल्प

• 2.4 × 10^-11 T

• 2.79 × 10^-5 T

• 2.79 × 10^-4 T

• 2.79 × 10^-3 T

Answer 1

A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is 2.79 × 10^-4 T.

Explanation:

Given, number of turns, n = 100,

radius of coil, r = 9 cm = 9 × 10^-2 m

and current flow in the coil, I = 0.4 A

The magnitude of the magnetic field at the centre of a coil of n turns is given by

B = ${\displaystyle \frac{{\mu }_0\text{nl}}{\text{2r}}}$     ....(i)

Substituting given values in Eq. (i), we get

${\displaystyle \Rightarrow \text{B}=\frac{12.56\times {10}^{-7}\times 100\times 0.4}{2\times {10}^{-1}\times 9\times {10}^{-2}}}$

= 2.79 × 10^-4 T