Question

Find the percent increase in the magnetic field $B$ when the space within a current-carrying toroid is filled with aluminum. The susceptibility of aluminum is $2.1\times {10}^{-5}$.

Answer 1

$B=\mu x$ (in Aluminum)
$={\mu }_0(1+R_m)4$
Increase in magnetic field
$=B-B_v={\mu }_0{x}_{m}4$
$increase=\frac{B-B_0}{B_0}\times 100$
$=\frac{{\mu }_0{x}_{m}4}{{\mu }_{0}4}\times 100=2.1\times {10}^{-5}\times 100=2.1\times {10}^{-3}$.