Question

A solenoid has $1000$ turns and $20\text{cm}$ long. Find the magnetic induction produced at the centre of the solenoid by the current of $2\text{A}$.

• A. $1.25\times {10}^{-3}\text{T}$
• B. $3.75\times {10}^{-2}\text{T}$
• C. $2.50\times {10}^{-2}\text{T}$
• D. $1.25\times {10}^{-2}\text{T}$

Answer 1

The correct option is D $1.25\times {10}^{-2}\text{T}$

Given:
$N=1000;l=20\text{cm}=0.2\text{m};i=2\text{A}$

Magnetic field at the centre of long solenoid is given by

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

$B={\mu }_0\left(\frac{N}{l}\right)i$

$B=4\pi \times {10}^{-7}\times \frac{1000}{0.2}\times 2$

$B=4\times 3.14\times {10}^{-3}=1.25\times {10}^{-2}\text{T}$

Hence, option $\left(d\right)$ is correct.