JEE Physics 2025 Question with Solution

Given: magnetic susceptibility of magnesium is $\chi_{mg} = 1.2 \times 10^{-5}$.

Find: percentage increase in magnetic field $B$ inside the solenoid when magnesium is inserted.

For a solenoid, inserting a material of susceptibility $\chi$ changes the field as

$$B' = B(1 + \chi_{mg})$$

Therefore, the fractional increase in magnetic field is

$$\frac{B' - B}{B} = \chi_{mg}$$

Hence, percentage increase is

$$\text{Percentage increase} = \chi_{mg} \times 100$$

Substituting the given value,

$$\text{Percentage increase} = 1.2 \times 10^{-5} \times 100 = 1.2 \times 10^{-3} \%$$

Now,

$$1.2 \times 10^{-3} = \frac{6}{5} \times 10^{-3}$$

Therefore, the percentage increase in magnetic field is $\frac{6}{5} \times 10^{-3} \%$ and the correct option is A.

Given: $\chi_{mg} = 1.2 \times 10^{-5}$.

Find: percentage increase in $B$.

Since

$$\mu_r = 1 + \chi$$

the percentage increase in magnetic field for a weakly magnetic material is directly

$$\chi \times 100$$

So,

$$1.2 \times 10^{-5} \times 100 = 1.2 \times 10^{-3} \%$$

Thus, the correct option is A.