Question

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

• A. $1.1\times {10}^{-3}$
• B. $2.1\times {10}^{-3}$
• C. $3.1\times {10}^{-3}$
• D. $4.1\times {10}^{-3}$

Answer 1

The correct option is B $2.1\times {10}^{-3}$

Given,
Susceptibility of aluminium, $\chi =2.1\times {10}^{-5}$

In the absence of aluminium, the magnetic field is,

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

As the space inside the toroid is filled with aluminium, the field becomes

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

The increase in the field is,

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

The percent increase is,

$\frac{B-B_0}{B_0}\times 100=\frac{{\mu }_0\chi H}{{\mu }_{0}H}\times 100$

$=\chi \times 100=2.1\times {10}^{-3}$

Hence, option $\left(B\right)$ is correct.