Question

The magnetic field inside a long solenoid is increased from $2\times {10}^{-3}\text{T}$ to $2.5\text{T}$ when an iron core is inserted in it. Find the relative permeability of the iron core.

Answer 1

Initially,

$B_1={\mu }_{o}H$

Finally, when an iron core is inserted,

$B_2=\mu H={\mu }_o{\mu }_{r}H$

$\therefore \frac{B_1}{B_2}=\frac{1}{{\mu }_r}$

$\frac{2.5\times {10}^{-3}}{2.5}=\frac{1}{{\mu }_r}$

$\therefore {\mu }_r=1000$

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