Question

The mutual inductance between two coplanar concentric rings A and B of radii 'R₁' and 'R₂' placed in air when a current 'I' flows through ring A is (R₁ >> R₂) (µ₀ = permeability of free space) ____________.

Options

• `(mu_0 pi "R"_2)/"R"_1`

• `(mu_0 pi "R"_1)/"R"_2`

• `(mu_0 pi "R"_1^2)/(2"R"_2)`

• `(mu_0 pi "R"_2^2)/(2"R"_1)`

Answer 1

The mutual inductance between two coplanar concentric rings A and B of radii 'R₁' and 'R₂' placed in air when a current 'I' flows through ring A is `(mu_0 pi "R"_2^2)/(2"R"_1)`.

Explanation:

Magnetic field produced by ring A and its centre is

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

Magnetic flux passing through ring B is

`phi_2 = "B"_1 pi"R"_2^2`

`= (mu_0 "I")/(2 "R"_1). pi"R"_2^2`

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

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