The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility \(\left.\chi_{\mathrm{mg}}=1.2 \times 10^{-5}\right)\) is :

\(\begin{aligned} & \% \text { change in } B=\frac{B_{\text {new }}-B_{\text {old }}}{B_{\text {old }}} \times 100 \% \\ & =\frac{\mu \mathrm{ni}-\mu_0 \mathrm{ni}}{\mu_0 \mathrm{ni}} \times 100 \%=\frac{\left(\mu-\mu_0\right)}{\mu_0} \times 100 \% \\ & =\frac{\left(\mu_0 \mu_{\mathrm{r}}-\mu_0\right)}{\mu_0} \times 100 \% \\ & =\left(\mu_{\mathrm{r}}-1\right) \times 100 \% \\ & =\chi_{\mathrm{n}} \times 100 \% \\ & =1.2 \times 10^{-3} \%\end{aligned}\)