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:
Answer & explanation
Correct answer: option 4
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,
$M=(4π×10^{-7})×\frac{1200}{7}×\frac{1000}{7}×π×(0.04)^2×7$
$≃1.08mH$