Question

A solenoid of length $20 cm ,$ area of cross-section $4 cm ^{2}$ and having $4000$ turns is placed inside another solenoid of $2000$ turns having a cross-sectional area of $8 cm ^{2}$ and length $10 cm$. 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)

$\ell=20 cm \Rightarrow 20 \times 10^{-2} m$
$\Rightarrow 0.2 m $
$A =4 cm ^{2}$
$\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)