Question

An iron rod of volume $10^{-3} m ^{3}$ and relative permeability $1000$ is placed as core in a solenoid with $10$ turns/cm. If a current of $0.5 \,A$ is passed through the solenoid, then the magnetic moment of the rod will be :

• A. $0.5 \times 10^{2} Am ^{2}$
• B. $50 \times 10^{2} Am ^{2}$
• C. $500 \times 10^{2} Am ^{2}$
• D. $5 \times 10^{2} Am ^{2}$

Answer 1

Answer: (D)

$M =\mu_{ r } NiA$
Here
$\mu_{ r }=$ Relative permeability
$N = No .$ of turns
$i =$ Current
$A=$ Aea of cross section
$M =\mu_{ r } Ni A =\mu_{ r } n \ell i A$
$ M =\mu_{ r } niV = 1000(1000) 0.5\left(10^{-3}\right) $
$=500=5 \times 10^{2} Am ^{2}$