Q 12-05-054JEE MainJEE Main 2021 (31 Aug, Shift 2)Medium
A long solenoid with $1000$ turns $\text{m}^{-1}$ has a core material with relative permeability $500$ and volume $10^3\ \text{cm}^3$. 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 $\dfrac{x}{499}$. Find the value of $x$.
Numerical value type. Enter your answer.
Answer: 250
Magnetic moment of the core $= MV = \chi HV$, and $H = nI$ is unchanged.
$\chi_1 = 500 - 1 = 499$, $\chi_2 = 750 - 1 = 749$.
$$\frac{\Delta m}{m} = \frac{749 - 499}{499} = \frac{250}{499} \Rightarrow x = 250$$
Solution by Sreeraj P, M.Sc Physics