Question

Two concentric circular coils having radii r₁ and r₂, (r₂ << r₁) are placed co-axially with centers coinciding. The mutual induction of the arrangement is (Both coils have a single turn) (µ₀ = permeability of free space).

Options

• `(mu_0 pi "r"_1^2)/(2"r"_2)`

• `(mu_0 pi "r"_2^2)/"r"_1`

• `(mu_0 pi "r"_2^2)/(2"r"_1)`

• `(pi_0 pi "r"_1^2)/"r"_2`

Answer 1

`(mu_0 pi "r"_2^2)/(2"r"_1)`

Explanation:

If current I₁ flows in the coil of radius r₁, the magnetic field at the center is given by

`"B"_1 = (mu_0 "I"_1)/(2"r"_1)`

The magnetic flux passing through the coil of radius r₂ will be

`phi_2 = "B"_1 xx pi"r"_2^2`

`= (mu_0 "I"_1)/(2"r"_1) xx pi"r"_2^2`

`"Mutual inductance M" = phi_2/"I"_1`

` = (mu_0 pi "r"_2^2)/(2"r"_1)`