Question

A conducting wire of 100 turns is wound over 1 cm near the centre of a solenoid of 100 cm length and 2 cm radius having 1000 turns. The mutual inductance of the two coils is

• A. 1.58 x 10-4 V
• B. 1.58 x10-3 V
• C. 2.11 x 10-4 V
• D. 2.11 x 10-3 V

Answer 1

Answer: (A)

1.58 x 10-4 V

Answer 2

Here , $N_{1} = 1000,l = 100cm = 1m$

$A = \pi r^{2} = \pi \times (2 \times 10^{- 2})^{2}m^{2}$

$N_{2} = 100$

$M = \mu_{0}\frac{N_{1}N_{2}A}{l}$

$= \frac{4\pi \times 10^{- 7} \times 1000 \times 100 \times \pi \times 4 \times 10^{- 4}}{1}$

$= 16\pi r^{2} \times 10^{- 6} = 16 \times 9.87 \times 10^{- 6}$

$= 1.58 \times 10^{- 4}V$