Question

A long cylindrical iron core of cross-sectional area $5.00{\text{cm}}^2$ is inserted into a long solenoid having $2000\text{turns/m}$ and carrying a current $2\text{A}$. The magnetic field inside the core is found to be $1.57\text{T}$. Neglecting the end effects, find the magnetization $I$ of the core and the pole strength developed

• A. $4.25\times {10}^6\text{A/m},125\text{Am}$
• B. $2.50\times {10}^6\text{A/m},125\text{Am}$
• C. $2.50\times {10}^6\text{A/m},625\text{Am}$
• D. $1.25\times {10}^6\text{A/m},625\text{Am}$

Answer 1

The correct option is D $1.25\times {10}^6\text{A/m},625\text{Am}$

The magnetic intensity $H$ inside the solenoid is,

$H=ni$

$\Rightarrow H=2000\times 2=4000{\text{Am}}^{-1}$

We know that,

$B={\mu }_0(H+I)$

$\Rightarrow I=\frac{B}{{\mu }_0}-H=\frac{1.57}{4\pi \times {10}^{-7}}-4000$

$=1.25\times {10}^6-4000$

$\approx 1.25\times {10}^6{\text{Am}}^{-1}$

The pole strength developed at the end is,

$m=IA$

$=(1.25\times {10}^6)\times (5\times {10}^{-4})$

$=625\text{Am}$

Hence, option $\left(D\right)$ is the correct answer.