Question

The percentage increase in magnetic field B when the space within a current carrying toroid is filled with aluminium ($\chi =2.1\times 10-5$) is?

• A. $0.2\%$
• B. $2\times {10}^{-3}\%$
• C. $2\times {10}^{-2}\%$
• D. $2\times {10}^{-4}\%$

Answer 1

The correct option is B $2\times {10}^{-3}\%$

Given:

The susceptibility of the aluminium is $2.1\times {10}^{-5}$.

The magnetic field in the absence of the aluminium:

$B_0={\mu }_{0}H$

Whereas the magnetic field in the presence of aluminium is:

$B={\mu }_0(1+{\chi }_m)H$

Therefore, the change in the magnetic field is given by:

$B-B_0={\mu }_0{\chi }_{m}H$

So, The percentage increase in the magnetic field is:

$\%B=\frac{{\mu }_0{\chi }_{m}H}{{\mu }_{0}H}\times 100\%$

$\%B={\chi }_m\times 100\%$

$⟹2.1\times {10}^{-3}\%$