Question

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

• A. $1:1$
• B. $1:4$
• C. $\sqrt{3}:2$
• D. $\sqrt{3}:1$

Answer 1

Answer: (D)

$F=\frac{k(2)(2)}{(1{)}^2}$
$(F=$ Force between two charges $)$.
$F=4k$
$F_{\text{net }}=2F\cos 30^{\circ }=2\cdot F\cdot \frac{\sqrt{3}}{2}=F\sqrt{3}$
$(F_{\text{net }}=$ Net electrostatic force on one charged ball $)$
$\frac{F_{\text{net }}}{F}=\frac{\sqrt{3}F}{F}=(\sqrt{3})$
Remark: Net force on any one of the ball is zero. But no option given in options.