Question

A solenoid has core of a material with relative permeability $500$ and its windings carry a current of $1A$. The number of turns of the solenoid is $500$ per metre. The magnetization of the material is nearly

• A. $2.5\times 10^{3}A{m}^{-1}$
• B. $2.5\times 10^{5}A{m}^{-1}$
• C. $2.0\times 10^{3}A{m}^{-1}$
• D. $2.0\times 10^{5}A{m}^{-1}$

Answer 1

Answer: (B)

Here, $n=500$ turns/m
$I=1A,{\mu }_r=500$
Magnetic intensity,
$H=nI=500m^{-1}\times 1A=500A{m}^{-1}$
As ${\mu }_r=1+\chi$
where $\chi$ is the magnetic susceptibility of the material
or $\chi =\left({\mu }_r-1\right)$
Magnetisation,
$M=\chi H$
$=\left({\mu }_r-1\right)H$
$=\left(500-1\right)\times 500A{m}^{-1}$
$=499\times 500A{m}^{-1}$
$=2.495\times 10^{5}A{m}^{-1}$
$\approx 2.5\times 10^{5}A{m}^{-1}$