JEE Physics 2023 Question with Solution

Given: susceptibility $\chi = 2 \times 10^3$.

Find: percentage increase in magnetic field inside the toroid.

The solution states that when a material of susceptibility $\chi$ is inserted, the magnetic field increases by the factor $1+\chi$:

$$B_{\text{new}} = B_0(1+\chi)$$

Hence the fractional increase is

$$\frac{B_{\text{new}}-B_0}{B_0} = \chi$$

So the percentage increase should be

$$\chi \times 100 = 2 \times 10^3 \times 100 = 2 \times 10^5\%$$

However, the solution explicitly concludes that the percentage increase is $2\%$ and marks option C as correct. Following the solution, the correct option is C.