Question

A short solenoid of length $4cm$, radius $2cm$ and $100$ turns is placed inside and on the axis of a long solenoid of length $80cm$ and $1500$ turns. A current of $3A$ flows through the short solenoid. The mutual inductance of two solenoids is

• A. $0.012H$
• B. $5.3\times {10}^{-5}H$
• C. $5.91\times {10}^{-3}H$
• D. $8.3\times {10}^{-5}H$

Answer 1

Answer: (C)

$5.91\times {10}^{-3}H$

As $M=\frac{{\mu }_0{N}_1{N}_{2}A}{l}$

where,

$A=$ common cross-sectional area

$l=$ length of small coil

$N_1=$ No. of turns of small coil

$N_1=$ No. of turns of long coil

$M=\frac{4\pi \times {10}^{-7}\times 100\times 1500\times \pi \times (\frac{2}{100}{)}^2}{\left(\frac{4}{100}\right)}=59157.6\times {10}^{-7}=5.91\times {10}^{-3}H$