Three identical charged balls each of charge $$2C$$ are suspended from a common point $$P$$ by silk threads of $$2$$ m each (as shown in figure). They form an equilateral triangle of side $$1$$ m. The ratio of net force on a charged ball to the force between any two charged balls will be

Here $$B_1,\ B_2,and\ B_3$$​ form an equilateral triangle.

Let the force between any two balls be F.

Consider ball $$B_1$$. It experiences two repulsive forces:

• Force F due to $$B_2$$​
• Force F due to $$B_3$$

These two forces act along $$B_1B_2\ and\ B_1B_3$$

Since $$B_1B_2B_3$$​ is an equilateral triangle, the angle between these two forces is

$$60^{\circ}$$

Hence the resultant force on $$B_1$$ is

$$R=\sqrt{F^2+F^2+2F^2\cos60^{\circ}}$$

$$R=\sqrt{2F^2+F^2}$$

$$R=\sqrt{3}F$$

Therefore,

Net force on one ballForce between any two balls=

$$\frac{\text{Net force on one ball}}{\text{Force between any two balls}}=\frac{\sqrt{\ 3}F}{F}$$

$$=\sqrt{3}:1$$

Hence the required ratio is