A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 10^3 cm^3. If the core material is replaced by…

A long solenoid with $\displaystyle 1000$ turns/m has a core material with relative permeability $\displaystyle 500$ and volume $\displaystyle 10^3 \mathrm{~cm}^3$. If the core material is replaced by another material having relative permeability of $\displaystyle 750$ with same volume maintaining same current of $\displaystyle 0.75$ A in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\displaystyle \left(\frac{x}{499}\right)$. Find the value of $\displaystyle x$.