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: , 2
(2) Given,
Volume of iron rod, $V=10^{-3} \mathrm{~m}^{3}$
Relative permeability, $\mu_{r}=1000$
Number of turns per unit length, $n=10$
Magnetic moment of an iron core solenoid,
$M=\left(\mu_{r}-1\right) \times N i A$
$\Rightarrow M=\left(\mu_{r}-1\right) \times N i \frac{V}{l} \Rightarrow M=\left(\mu_{r}-1\right) \times \frac{N}{l} i V$
$\Rightarrow M=999 \times \frac{10}{10^{-2}} \times 0.5 \times 10^{-3}=499.5 \approx 500$
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