Question

A long solenoid with $1000$ turns/m 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 $0.75\text{A}$ 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 $x$.

• A. 250.00
• B. 250
• C. 250.0

Answer 1

Answer: (A), (B), (C)

Magnetic moment is given by $m=({\mu }_r-1)NiV$
Here ${\mu }_r$ is relative permeability,
$N$ is number of turns
$i$ current in the coil

Now fractional change in magnetic moment is $\frac{\Delta m}{m}=\frac{750-1-(500-1)}{500-1}=\frac{250}{499}$

Given that, fractional change in magnetic moment is equal to $\left(\frac{x}{499}\right)=\frac{250}{499}$

Hence $x=250,250.0,250.00$