JEE Physics 2025 Question with Solution

Given: A square loop of side $a = 1 \, \text{m}$ is placed normally in front of a point charge $q = 1 \, \text{C}$. The flux through the shaded region is written as $\frac{5}{p} \times \frac{1}{\varepsilon_0}$.

Find: The value of $p$.

The solution states that the electric flux through a surface is related to the solid angle subtended by that surface. It also explicitly marks option C as the correct option.

Using the working shown in the second approach:

$$\Phi_{\text{total}} = \frac{q}{\varepsilon_0} \times \frac{1}{6}$$

The square is divided into 8 equal parts, and the shaded region corresponds to 5 of those parts. Therefore,

$$\Phi_{\text{shaded}} = \frac{5}{8} \times \Phi_{\text{total}}$$

Substituting the expression for total flux,

$$\Phi_{\text{shaded}} = \frac{5}{8} \times \frac{q}{\varepsilon_0} \times \frac{1}{6}$$

So,

$$\Phi_{\text{shaded}} = \frac{5}{48} \times \frac{q}{\varepsilon_0}$$

With $q = 1 \, \text{C}$,

$$\Phi_{\text{shaded}} = \frac{5}{48} \times \frac{1}{\varepsilon_0}$$

Comparing with the given expression,

$$\frac{5}{p} \times \frac{1}{\varepsilon_0} = \frac{5}{48} \times \frac{1}{\varepsilon_0}$$

Hence,

$$p = 48$$

the solution is internally inconsistent because it concludes 48, while the listed options do not contain 48 and the page also labels option C as correct. Following the page's marked correct option, the answer is taken as C. The value in option C is $12 \, \text{N/m}^2$, though the extracted working indicates $p = 48$.

Given: the solution uses a symmetry-based partition of the flux.

Find: Match the form $\frac{5}{p} \times \frac{1}{\varepsilon_0}$.

The hint says that flux through the surface is proportional to the solid angle subtended by that region. The second approach then treats the relevant square flux as

$$\frac{q}{\varepsilon_0} \times \frac{1}{6}$$

and divides that square into 8 equal parts.

Since the shaded part contains 5 such equal parts,

$$\Phi_{\text{shaded}} = \frac{5}{8} \times \frac{q}{6\varepsilon_0}$$

Therefore,

$$\Phi_{\text{shaded}} = \frac{5q}{48\varepsilon_0}$$

For $q = 1$,

$$\Phi_{\text{shaded}} = \frac{5}{48} \times \frac{1}{\varepsilon_0}$$

Thus the comparison gives

$$p = 48$$

However, because the solution's simultaneously declares The Correct Option is C, the extracted MCQ answer is recorded as C.