JEE Physics 2026 Question with Solution

Given: Five identical positive charges of magnitude $q$ are placed at the vertices of a regular pentagon, each at distance $r$ from the center $O$.

Find: The electric potential $V$ and electric field $\vec{E}$ at the center.

Step 1: Electric potential at the center

Electric potential is a scalar quantity, so the contributions add algebraically.

Potential due to one charge at the center is

$$V_1 = \frac{q}{4\pi\varepsilon_0 r}$$

For five identical charges,

$$V = 5V_1 = \frac{5q}{4\pi\varepsilon_0 r}$$

Step 2: Electric field at the center

Electric field is a vector quantity. The fields due to the five charges at the center have equal magnitude and are symmetrically distributed in direction.

By regular pentagonal symmetry, the vector sum cancels:

$$\vec{E} = 0$$

Conclude: Therefore, the electric potential is $\dfrac{5q}{4\pi\varepsilon_0 r}$ and the electric field is $0$. The correct option is D.