Physics - Magnetism Question with Solution | TestHub

The initial magnetic field in the toroid without the core is $B_0={\mu }_{0}nI$.

When the space is filled with aluminium of susceptibility $\chi$, the magnetic field becomes $B={\mu }_0{\mu }_{r}nI$.

The relative permeability is related to susceptibility as ${\mu }_r=1+\chi$.

Thus, $B={\mu }_0(1+\chi )nI=B_0(1+\chi )=B_0+B_0\chi$.

The increase in the magnetic field is $\Delta B=B-B_0=B_0\chi$.

The percentage increase in the magnetic field is $\frac{\Delta B}{B_0}\times 100=\frac{B_0\chi }{B_0}\times 100=\chi \times 100$.

Answer: $\chi \times 100$