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 \({x}\).

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Correct Answer

(D) \(250\)

Step-by-step Solution

Detailed explanation

\(\frac{\Delta {M}}{{M}}=\frac{\Delta \mu}{\mu}=\frac{250}{500}=\frac{1}{2}\)

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

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