Q 12-05-083JEE MainJEE Main 2025 (7 Apr, Shift 1)Easy
The percentage increase in magnetic field ($B$) when the space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{mg} = 1.2\times10^{-5}$) is:
Answer: (A) $\dfrac65\times10^{-3}\%$
Inside the solenoid $B = \mu_0\mu_r nI$, so filling it changes $B$ by the factor $\mu_r = 1 + \chi$:
$$\frac{\Delta B}{B}\times100\% = (\mu_r - 1)\times100\% = \chi\times100\% = 1.2\times10^{-3}\% = \frac65\times10^{-3}\%$$
Solution by Sreeraj P, M.Sc Physics