Question

A solenoid of $1000$ turns per metre has a core with relative permeability of $500$. Insulated windings of the solenoid carry an electric current of $5\text{A}$. The magnetic flux density produced by the solenoid is -

$($Permeability of free space $=4\pi \times {10}^{-7}\text{H/m})$

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

Answer 1

The correct option is D $\pi \text{T}$

Given :
$I=5\text{A}n=1000{\text{m}}^{-1}{\mu }_r=500{\mu }_o=4\pi \times {10}^{-7}\text{H/m}$

Magnetic flux density,
$B=\mu nI$
$\Rightarrow B={\mu }_r{\mu }_{0}nI$
$\Rightarrow B=500\times 4\pi \times {10}^{-7}\times {10}^3\times 5$
$\Rightarrow B=\pi \text{T}$

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