Question

A solenoid of length $1.5m$ and $4cm$ in diameter possesses $10turns$ per metre. A current of $5A$ is flowing through it. The magnetic induction at a point inside the solenoid along the axis is _______$({\mu }_0=4\pi \times {10}^{-7}Wb/A.m)$

• A. $\pi \times {10}^{-5}T$
• B. $2\pi \times {10}^{-5}T$
• C. $3\pi \times {10}^{-5}T$
• D. $4\pi \times {10}^{-5}T$

Answer 1

The correct option is B $2\pi \times {10}^{-5}T$

Consider the problem

Given,

$l=1.5m$

$N=\frac{n}{l}=10$

$I=5A$

${\mu }_0=4\pi \times {10}^{-7}Wb/A.m$

And

$r=\frac{d}{2}=2cm=0.02m$

Now, the magnetic field inside the solenoid is

$\begin{array}{c}B={\mu }_{0}NI={\mu }_0\frac{n}{l}I\\ =\pi \times {10}^{-7}\times 10\times 5\\ =2\pi \times {10}^{-5}T\end{array}$

Hence, Option $B$ is the correct answer.