Question

For the given arrangement of charges, find the strength of electric field \( E \) and potential \( V \) at the geometrical center \( O \).

• A. \( E = 0; V = 0 \)
• B. \( E = 0; V = \text{Non-zero} \)
• C. \( E = \text{Non-zero}; V = \text{Non-zero} \)
• D. \( E = \text{Non-zero}; V = 0 \)

Hint:

In symmetrical charge distributions, the electric field at the center cancels out, but the electric potential remains non-zero.

Answer 1

The Correct Option is B

Step 1: Electric field at the center of symmetry.
In the case of charges arranged symmetrically, the electric field at the center of the configuration cancels out due to symmetry. In this case, since the charges are placed symmetrically, the net electric field at the center will be zero. Step 2: Electric potential at the center.
The electric potential, on the other hand, is a scalar quantity and does not cancel out due to symmetry. The potential at the center will be the sum of the potentials due to each charge. Since the charges are equal and symmetrically arranged, the net potential at the center will be non-zero. Final Answer: \[ \boxed{E = 0; V = \text{Non-zero}}. \]