Question

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10{\text{cm}}^2$ and length $20\text{cm}$. It one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is

• A. $4.8\pi \times {10}^{-4}\text{H}$
• B. $2.4\pi \times {10}^{-4}\text{H}$
• C. $4.8\pi \times {10}^{-5}\text{H}$
• D. $2.4\pi \times {10}^{-5}\text{H}$

Answer 1

The correct option is B $2.4\pi \times {10}^{-4}\text{H}$

Mutual inductance $M=\frac{{\mu }_0{N}_1{N}_{2}A}{l}$
$M=\frac{4\pi \times {10}^{-7}\times 300\times 400\times 10\times {10}^{-4}}{20\times {10}^{-2}}$
$M=24\pi \times {10}^{-5}$
$M=2.4\pi \times {10}^{-4}\text{H}$