JEE Physics 2025 Question with Solution

Given: Two infinite identical charged sheets and a uniformly charged spherical body of volume charge density $\rho$ are placed as shown. Find: the correct relation among the electric fields at $A, B, C, D$.

For an infinite sheet of charge, the field magnitude is

$$E = \frac{\sigma}{2\varepsilon_0}$$

on each side. For a uniformly charged non-conducting sphere, the field inside increases with distance from the center, while outside it behaves like the field of a point charge at the center.

Between the two identical sheets, the fields due to the sheets cancel each other, so at points $A$ and $B$ the net field is mainly due to the charged sphere. Since the electric field inside the sphere increases with radial distance from the center, and $A$ is farther from the center than $B$, we get

$$E_A > E_B$$

At points $C$ and $D$, which are outside the sheets, the field due to the sheets is the same in magnitude in the corresponding outer regions, but the contribution from the sphere is in opposite directions relative to the sheet field. Hence the resultant fields at $C$ and $D$ are not equal.

$$E_C \neq E_D$$

Therefore, the correct option is C.