Question:
An iron rod of volume $10^{-3} \mathrm{~m}^{3}$ and relative permeability 1000 is placed as core in a solenoid with 10 turns $/ \mathrm{cm}$. If a current of $0.5 \mathrm{~A}$ is passed through the solenoid, then the magnetic moment of the rod will be :
Correct Option: , 4
Solution:
$\mathrm{M}=\mu_{\mathrm{r}} \mathrm{NiA}$
Here
$\mu_{\mathrm{r}}=$ Relative permeability
$\mathrm{N}=$ No. of turns
$\mathrm{i}=$ Current
$\mathrm{A}=$ Aea of cross section
$\mathrm{M}=\mu_{\mathrm{r}} \mathrm{NiA}=\mu_{\mathrm{r}} \mathrm{n} \ell \mathrm{i} \mathrm{A}$
$\mathrm{M}=\mu_{\mathrm{r}} \mathrm{niV}=1000(1000) 0.5\left(10^{-3}\right)$
$=500=5 \times 10^{2} \mathrm{Am}^{2}$