Question

A solenoid has core of a material with relative permeability $500$ and its windings carry a current of $1\, A$. 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
$I = 1 \,A, \mu_{r} = 500$
Magnetic intensity,
$H =nI= 500 \,m^{-1} \times 1 \,A = 500 \,A \,m^{-1}$
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 500\,A\,m^{-1}$
$= 499 \times 500\, A\, m^{-1}$
$ = 2.495 \times 10^{5} \,A \,m^{-1}$
$\approx 2.5 \times 10^{5}\,A\,m^{-1}$