# The value of aluminium

Question:

The value of aluminium susceptibility is $2.2 \times 10^{-5}$. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $\frac{x}{10^{4}}$. Then the value of $x$ is ______

Solution:

$\mathrm{B}=\mu .(\mathrm{H}+\mathrm{I})$

$\mathrm{B}=\mu . \mathrm{H}\left(1+\frac{\mathrm{I}}{\mathrm{H}}\right)$

$\mathrm{B}=\mathrm{B}_{0}(1+\mathrm{x})$

$\mathrm{B}-\mathrm{B}_{0}=\mathrm{B}_{0} \mathrm{x}$

$\frac{\mathrm{B}-\mathrm{B}_{0}}{\mathrm{~B}_{0}}=\mathrm{x}$

$\frac{\mathrm{B}-\mathrm{B}_{0}}{\mathrm{~B}_{0}} \times 100=100 \mathrm{x}$

$=2.2 \times 10^{-3}=\frac{22}{10^{4}}$