Question

Two ball $A$ and $B$ of same mass $\left(M\right)$ and charges $Q,-Q$ are suspended by two strings of same length from two different suspension points $S_1$ and $S_2$ if $S_1{S}_2=3x$ and $AB=x$ then show that-
tension in the string is $T=\frac{Q^{2}L}{4\pi {\in }_0{x}^3}$
$\tan \theta =\frac{Q^2}{4\pi {\in }_0{x}^{2}Mg}$

Answer 1

Angle $\theta$ is not defined from where it is measure in complete question .

let angle made by eachh string is $\theta$ with vertical

$sin\theta =\frac{x}{L}$from the forces .

force by electrostat F = $\frac{K{Q}^2}{x^2}$

F = t sin $\theta$

$\frac{K{Q}^2}{sin\theta x^2}$ = T

T = $\frac{K{Q}^2}{\left(\frac{x}{L}\right)x^2}$ tension in the string

T cos$\theta =Mg$

divide both the eqn

$tan\theta =\frac{F}{Mg}$

= $\frac{\frac{K{Q}^2}{x^2}}{Mg}$

= $\frac{K{Q}^2}{Mg{x}^2}$