JEE Main 2025 Apr 7 Shift 1, Physics Q7: Magnetism and Matter

Inside a long solenoid, the field is $B=\mu ni$ with a medium and $B_0={\mu }_{0}ni$ in vacuum. The fractional change on filling with a linear medium is

$\frac{B-B_0}{B_0}=\frac{\mu -{\mu }_0}{{\mu }_0}={\mu }_r-1={\chi }_m$

Substituting the given susceptibility:

$\frac{\Delta B}{B_0}\times 100\%={\chi }_m\times 100\%=1.2\times 10^{-5}\times 100\%=1.2\times 10^{-3}\%$

Rewriting $1.2=6/5$:

$\text{Percentage change}=\frac{6}{5}\times 10^{-3}\%$

$\therefore$ Option (1).