Question

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

• A. $300A{m}^{-1}$
• B. $30000A{m}^{-1}$
• C. $30000\pi A{m}^{-1}$
• D. $3\pi A{m}^{-1}$

Answer 1

The correct option is B $30000A{m}^{-1}$

magnetic moment of solenoid is given as $NiA$ where N is total number of turns and A is current in coil and A is area of coil o solenoid.
As the solenoid is equivalent of magnet of same size, their magnetic moment will be equal
$\overrightarrow{m}=Ni\overrightarrow{A}$
Magnetization $\overrightarrow{M}=\frac{\overrightarrow{m}}{V}=\frac{\overrightarrow{m}}{Al}=\frac{Ni}{l}$
Substituting $N=500,i=15A,l=.25m$
$\overrightarrow{M}=30,000A{m}^{-1}$ Hence, correct answer is option B.