JEE Physics 2023 Question with Solution

Given: cross-sectional area $A = 2 \times 10^{-4} \, \text{m}^2$, length $l = 0.40 \, \text{m}$, number of turns $N = 400$, current $I = 0.4 \, \text{A}$, magnetic flux $\phi = 4 \times 10^{-6} \, \text{Wb}$, and $\mu_0 = 4\pi \times 10^{-7} \, \text{N/A}^2$.

Find: the relative permeability $\mu_r$ of the rod.

From the solution, the magnetic flux inside the winding is written as

where $n = 400$ and $l = 0.40 \, \text{m}$.

Substituting the given values as shown:

With $\phi = 4\pi \times 10^{-6}$, the extracted working concludes:

Therefore, the relative permeability of the rod is $125$. The solution explicitly states "The Correct Option is A", although the listed value $125$ appears as option C. the answer is marked as A with this discrepancy noted.

Given: magnetic flux relation from the solution uses

Hence,

with turn density effectively used as $\frac{400}{0.40}$ in the extracted steps.

The second approach in the solution writes:

Then it simplifies to

so that

Therefore, the relative permeability is $125$.