Question

A solenoid $600mm$ long has $50$ turns on it and is wound on an iron rod of $7.5mm$ radius. Find the flux through the solenoid when the current in it, is $3A$. The relative permeability of iron is $600$.

• A. $1.66Wb$
• B. $1.66nWb$
• C. $1.66mWb$
• D. $1.66\mu Wb$
• E. $1.66pWb$

Answer 1

The correct option is C

$1.66mWb$

Step 1: Given data

Length of a solenoid, $L=600mm$

Radius of the solenoid, $d=7.5mm=7.5\times {10}^{-3}m$

Current, $I=3A$

Total number of turns,$N=50$

Step 2: Find Magnetic flux

Magnetic flux through one loop is

$$\begin{gathered} \varphi =BA \\ \varphi =\frac{{\mu }_r{\mu }_0{N}^{2}AI}{L} \\ \varphi =\frac{600\times 4\mathrm{\pi }\times {10}^{-7}\times {50}^2\times \mathrm{\pi }\times {\left(7.5\times {10}^{-3}\right)}^2\times 3}{600\times {10}^{-3}} \\ \varphi =1.66x{10}^{-3}Wb \\ \varphi =1.66mWb \end{gathered}$$

Hence, option C is correct.