Question

The space within a current carrying toroid is filled with magnesium $\left(\chi =1.2\times {\left(10\right)}^{-5}\right)$ . The percentage increase in magnetic field B is $N\times 10^{-4}\%$ . The value of $N$ is

Answer 1

Answer: 12

Here, $\chi =1.2\times 10^{-5}$
From, $B={\left(\mu \right)}_0(H+I)$
$={\left(\mu \right)}_{0}H\left(1+\frac{I}{H}\right)=B_0(1+\chi )$
$\Rightarrow B-B_0=B_0\chi$
$\Rightarrow \frac{B-B_0}{B_0}=\chi$ $\Rightarrow \frac{B-B_0}{B_0}\times 100$ = $100\times \chi$
$=100\times 1.2\times 10^{-5}$ $=12\times 10^{-4}\%$