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

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