Question

A $25cm$ long solenoid has a radius of $2cm$ and $500$ total number of turns. It carries a current of $15A$. If it is equivalent to a magnet of the same size and magnetization $\overrightarrow{M}$ (magnetic moment / vloume), then $\left|\overrightarrow{M}\right|$ is

• A. $300A/m$
• B. $30000A/m$
• C. $30000\mathrm{\pi }A/m$
• D. $3\mathrm{\pi }\mathrm{A}/\mathrm{m}$

Answer 1

The correct option is B

$30000A/m$

Step 1: Given Data

Length of the solenoid $L=25cm=25\times {10}^{-2}m$

The radius of the solenoid $r=2cm$

Number of turns of the solenoid $n=500$

Current passing through the solenoid $I=15A$

Magnetization $\overrightarrow{M}=\frac{magneticmoment}{vloume}$

Step 2: Calculate the Magnetization

We know that magnetic moment $=nIA$

We know that volume $=AL$

$\therefore \left|\overrightarrow{M}\right|=\frac{nIA}{AL}$

$=\frac{nI}{L}$

Upon substituting the values we get,

$\left|\overrightarrow{M}\right|=\frac{500\times 15}{25\times {10}^{-2}}$

$=30000A/m$

Hence, the correct answer is option (B).