A long solenoid with 1000 turns/m has a core material with relative… | JEE Main 2021 (31 Aug, Shift 2)

Q43JEE Main 2021 · 31 AUG · SHIFT 2Medium

Ampere's Law, Cylinders, Solenoid & Toroid

A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 103 cm3. 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.

Numerical answer type. Work it out, then open the answer.

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Answer: 250

Moment of core $m = MV = (\mu_r - 1) n I V$ , so $m \propto (\mu_r - 1)$ for the same $n$ , $I$ , $V$ .
Fractional change $= \frac{(750 - 1) - (500 - 1)}{500 - 1} = \frac{250}{499}$
So $x = 250$ .

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