Question

Calculate the inductance of a solenoid containing 200 turns, a length of 25 cm and an area of cross section of $8c{m}^2$.

• A. $1.6\times {10}^{-4}H$
• B. $3.2\times {10}^{-4}H$
• C. $2.4\times {10}^{-4}H$
• D. $0.8\times {10}^{-4}H$

Answer 1

The correct option is A $1.6\times {10}^{-4}H$

$L={\mu }_0{n}^{2}V=4\pi \times {10}^{-7}\times n^2\times v$
n = no of turms in 1 metre
Given,
25 cm $\to$ 200 turms
so, $1m\to$ 800 turms
Therefore, n = 800
$V=A\times l=8\times {10}^{-4}\times 25\times {10}^{-2}=200\times {10}^{-4}\times {10}^{-2}=2\times {10}^{-4}$

$L=4\pi \times {10}^{-7}\times (800{)}^2\times 2\times {10}^{-4}$
$=4\pi \times {10}^{-7}\times 64\times {10}^4\times 2\times {10}^{-4}=4\times \frac{22}{7}\times 2\times 64\times {10}^{-7}$
$=1608\times {10}^{-7}=1.6\times {10}^{-4}H$