Q63 / 75 · JEE Main 2025 (7 Apr Shift 1) · Physics

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 :

  • Correct answer
    A
    $\frac{6}{5} \times 10^{-3} \%$
  • B
    $\frac{5}{6} \times 10^{-5} \%$
  • C
    $\frac{5}{6} \times 10^{-4} \%$
  • D
    $\frac{5}{3} \times 10^{-5} \%$

Solution

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

Hence, the correct answer is option: 'A'.

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