Question

An iron rod of volume ${10}^{-4}{\text{m}}^3$ and relative permeability $1000$ is placed inside a long solenoid wound with $5\text{turns/cm}$. If a current of $0.5\text{A}$ is passed through the solenoid, find the magnetic moment of the rod.

• A. $15{\text{Am}}^2$
• B. $20{\text{Am}}^2$
• C. $25{\text{Am}}^2$
• D. $30{\text{Am}}^2$

Answer 1

The correct option is C $25{\text{Am}}^2$

Given:
$n=5{\text{cm}}^{-1}=500\text{turns/m}$
$i=0.5\text{A}$

The magnetic intensity for a solenoid having $n\text{turns/ length}$ and current $i$ is,

$H=ni$

Substituting the values,

$\Rightarrow H=\left(500\right)\times 0.5=250\text{A/m}$

As, we know that magnetization of a magnet is,

$I=H({\mu }_r-1)$

$\Rightarrow I=250\times (1000-1)=2.49\times {10}^5\text{A/m}$

Using the relation, $I=\frac{M}{V}$, we have

$M=IV$

$=(2.49\times {10}^5)\times \left({10}^{-4}\right)$

$=24.9\approx 25{\text{Am}}^2$

Hence, option $\left(C\right)$ is correct.