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  4. A long solenoid with 1000 turns / m has a core material with relative permeability 500 and volume 103 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 A in the solenoid, the fractional change in the magnetic moment of the core would be approximately ((x/499)). Find the value of x.

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Q. 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 another material having relative permeability of $750$ with same volume maintaining same current of $0.75 \,A$ 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 $x$.

JEE MainJEE Main 2021Moving Charges and Magnetism

Solution:

$\frac{\Delta M }{ M }=\frac{\Delta \mu}{\mu}=\frac{250}{500}=\frac{1}{2}$
$\frac{1}{2}=\frac{ x }{499} \Rightarrow x \simeq 250$