Question

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____× 10^-8 H.
(Take, π² = 10)

Answer 1

Correct Answer: 4

Given, \[ a = 1000 \, \text{cm}, \quad b = 1 \, \text{cm} \] As the larger coil is taken as primary, \[ \text{Mutual inductance } M = \frac{\mu_0 N n b^2}{2a} \] \[ M = \frac{4\pi \times 10^{-7} \times 200 \times 10 \times \pi \times 1 \times 10^{-4}}{2 \times 1000 \times 10^{-2}} \] \[ M = 4 \times 10^{-8} \, \text{H} \] Therefore, the value of mutual inductance is 4 $\times 10^{-8$ H}.