Question

A solenoid of length $20cm,$ area of cross-section $4c{m}^2$ and having $4000$ turns is placed inside another solenoid of $2000$ turns having a cross-sectional area of $8c{m}^2$ and length $10cm$. What is the mutual inductance between two solenoids?

• A. $4\times 10^{-4}H$
• B. $2\times 10^{-3}H$
• C. $2\times 10^{-1}H$
• D. $2\times 10^{-2}H$

Answer 1

Answer: (D)

$\ell =20cm\Rightarrow 20\times 10^{-2}m$
$\Rightarrow 0.2m$
$A=4c{m}^2$
$\Rightarrow 4\times 10^{-4}{m}^2$
$N_1=4000,N_2=2000,M=?$
As, we know,
$M=\frac{{\mu }_0{N}_1{N}_{2}A}{\ell }$
$\Rightarrow \frac{4\pi \times 10^{-7}\times 2000\times 4000\times 4\times 10^{-4}}{20\times 10^{-2}}$
$=\frac{4\times 3.14\times 10^{-7}\times 8\times 4\times 10^{+6}\times 10^{-4}}{20\times 10^{-2}}$
$M=2\times 10^{-2}H$
(Area of smaller, length of longer solenoids are always considered)