Question

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ >> R₂, the mutual inductance M between them will be directly proportional to ______.

Options

• `"R"_1^2/"R"_2`

• `"R"_2^2/"R"_1`

• `"R"_1/"R"_2`

• `"R"_2/"R"_1`

Answer 1

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ >> R₂, the mutual inductance M between them will be directly proportional to `bbunderline("R"_2^2/"R"_1)`.

Explanation:

For two concentric coplanar loops with R1 >> R2

The magnetic field at the centre due to the larger loop is:

`B = (μ_0I)/(2R_1)`

Since the smaller loop lies well within the larger one, this field is approximately uniform over it.

Magnetic flux through the smaller loop:

`Φ = B xx "area" = (μ_0I)/(2R_1) · piR_2^2`

Mutual inductance:

`M = Φ/I = (μ_0piR_2^2)/(2R_1)`

So,

`M ∝ (R_2^2)/(R_1)`