Question

For the following diagram, determine the strength of the magnetic field at a point $\text{P}$ shown inside the solenoid if the number of turns per unit length are $500$ and a current of $0.5\text{A}$ is flowing through it.

• A. $2.14\times {10}^{-5}\text{T}$
• B. $2.14\times {10}^{-4}\text{T}$
• C. $2.14\times {10}^5\text{T}$
• D. $2.14\times {10}^{-3}\text{T}$

Answer 1

The correct option is B $2.14\times {10}^{-4}\text{T}$

Given:
$n=500;i=0.5\text{A};{\theta }_1={120}^{\circ };{\theta }_2={30}^{\circ }$


Magnetic field inside the solenoid at a point $P$ is given by

$B=\frac{{\mu }_{0}ni}{2}[\cos {\theta }_2-\cos {\theta }_1]$

$B=\frac{4\pi \times {10}^{-7}\times 500\times 0.5}{2}[\frac{\sqrt{3}}{2}+\frac{1}{2}]$

$B=2\pi \times {10}^{-7}\times 250\left[\frac{1.73+1}{2}\right]$

$\therefore B=21.4\times {10}^{-5}\text{T}$

Hence, option $\left(b\right)$ is the right answer.