A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume
Question:

A long solenoid with 1000 turns $/ \mathrm{m}$ has a core material with relative permeability 500 and volume $10^{3} \mathrm{~cm}^{3}$. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of $0.75 \mathrm{~A}$ in the solenoid, the fractional change in the magnetic moment of the core would be

approximately $\left(\frac{x}{499}\right)$. Find the value of $x$.

Solution:

$\frac{\Delta \mathrm{M}}{\mathrm{M}}=\frac{\Delta \mu}{\mu}=\frac{250}{500}=\frac{1}{2}$

$\frac{1}{2}=\frac{x}{499} \Rightarrow x \simeq 250$