A charge q is divided into three equal parts and placed symmetrically on a circle of radius r. The same charge is divided into four equal parts and placed symmetrically on the same circle. The electric field intensities at the centre of the circle in two situations are zero
Q. The ratio of electric potentials at the centre in the two situations is

Options

A. `(2)/(sqrt(3))`
B. `(1)/(1)`
C. `(4)/(3)`
D. `(16)/(9)`

Explanation

To solve the problem, we need to find the electric potentials at the center of a circle for two different scenarios where a charge \( Q \) is divided into three equal parts and four equal parts, respectively.

### Step-by-Step Solution:

1. **Understanding the Charge Distribution**:
- In the first case, the charge \( Q \) is divided into three equal parts. Each part will have a charge of \( \frac{Q}{3} \).
- In the second case, the charge \( Q \) is divided into four equal parts. Each part will have a charge of \( \frac{Q}{4} \).

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