Question

A long solenoid of $50\text{cm}$ length having $100$ turns carries a current of $2.5\text{A}.$ The magnetic induction at the center of the solenoid is $[{\mu }_0=4\pi \times {10}^{-7}{\text{T Am}}^{-1}]$

• A. $6.28\times {10}^{-4}\text{T}$
• B. $3.14\times {10}^{-4}\text{T}$
• C. $3.14\times {10}^{-5}\text{T}$
• D. $6.28\times {10}^{-5}\text{T}$

Answer 1

The correct option is A $6.28\times {10}^{-4}\text{T}$

Given, $N=100;l=50\text{cm}=\frac{1}{2}\text{m};n=\frac{N}{l}=\frac{100}{\left(\frac{1}{2}\right)}=200;i=2.5\text{A}$
$i=2.5A$

Magnetic induction at the center of the solenoid is,

$B={\mu }_{0}ni$

$=4\pi \times {10}^{-7}\times 200\times 2.5$

$=2\times 3.14\times {10}^{-4}$

$=6.28\times {10}^{-4}\text{T}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.