Question

Two concentric circular loops of radius 1 cm and 20 cm are placed coaxially.

1. Find mutual inductance of the arrangement.
2. If the current passed through the outer loop is changed at a rate of 5 A/ms, find the emf induced in the inner loop. Assume the magnetic field on the inner loop to be uniform.

Answer 1

i. M = `(mu_0 pi r^2)/(2 R)`

μ₀ = 4π × 10⁻⁷

r = 1 cm = 0.01 m

R = 20 cm = 0.2 m

Putting the values,

M = `(4 pi xx 10^-7 xx pi(0.01)^2)/(2 xx 0.2)`

= 0.00986 × 10⁻⁷ H

= 9.98 × 10⁻⁴ H

ii. |e| = `M (Delta i)/(Delta t)`

Or, |e| = 9.98 × 10⁻⁴ H × 5000 A/s

∴ Induced emf (|e|) = 9.98 × 0.5

= 4.99 V