Question

A solenoid of $1000$ turns per metre has a core with a relative permeability of $500$. Insulated windings of the solenoid carry an electric current of $5A$. The magnetic flux density produced by the solenoid is: (Permeability of free space $=4\times {10}^{-7}H/m$)

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

Answer 1

The correct option is D

$\pi T$

Step 1: Given data

Total number of turns per metre,

$n=1000$

Permeability of free space ${\mu }_0=4\times {10}^{-7}H/m$

Electric current $I=5A$

Step 2: Find magnetic flux density

Magnetic flux density will be,

$$\begin{gathered} B=\mu nI \\ B={\mu }_r{\mu }_{0}nI \\ B=500\times 4\pi \times {10}^{-7}\times {10}^3\times 5 \\ B=\pi \times {10}^{-3}\times {10}^3 \\ B=\pi T \end{gathered}$$

Hence, option D is correct.