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. If a charge (part charge) is removed from one location in both the situations, the ratio of magnitudes of the electric field intensities at the centre is

Options

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

Explanation

To solve the problem step by step, we will analyze the electric field intensities at the center of the circle for both cases when one charge is removed.

### Step 1: Understand the Configuration
We have two scenarios:
1. A charge \( Q \) is divided into three equal parts, \( \frac{Q}{3} \), and placed symmetrically on a circle of radius \( r \).
2. The same charge \( Q \) is divided into four equal parts, \( \frac{Q}{4} \), and placed symmetrically on the same circle.

In both cases, the electric field at the center of the circle is zero due to symmetry.
...