Two solenoids each of length 7 m are placed co-axially, the outer solenoid has 1000 turns and the inner solenoid has 1200 turns. The diameter of the inner solenoid is 8 cm. The mutual inductance between the two solenoids is:

$1.08 \times 10^{-3} H$

The correct answer is Option (4) → $1.08 \times 10^{-3} H$

Mutual Induction (M) between two solenoids can be calculated using -

$M=μ_0n_1n_2Al$

where,

$n_1$ → number of turns per unit length of solenoid.

$n_2$ → number of turns per unit length of outer solenoid.

$A$ → Area of cross - section.

$l$ → length of each solenoid.

$l=7cm$

$N_1=1200$

$N_2=1000$

$r=\frac{d}{2}=\frac{0.08}{2}=0.04m$

$n_1=\frac{N_1}{l}=\frac{1200}{7}$

$n_2=\frac{N_2}{l}=\frac{1000}{7}$

and,

$M=(4π×10^{-7})×\frac{1200}{7}×\frac{1000}{7}×π×(0.04)^2×7$

$≃1.08mH$