Question

A pendulum bob of mass $m$ carrying a charge $q$ is at rest with its string making an angle $\theta$ with the vertical in a uniform horizontal electric field $E$. The tension in the string is

• A. $\frac{mg}{\sin \theta }$
• B. $mg$
• C. $\frac{qE}{\sin \theta }$
• D. $\frac{qE}{\cos \theta }$

Answer 1

The correct option is C $\frac{qE}{\sin \theta }$

We can draw the forces acting on the bob as shown,


On applying Lami's theorem:

$\frac{T}{\sin 90}=\frac{qE}{\sin (180-\theta )}=\frac{mg}{\sin (90+\theta )}$

$\Rightarrow \frac{T}{1}=\frac{qE}{\sin \theta }=\frac{mg}{\cos \theta }$

$\Rightarrow T=\frac{qE}{\sin \theta }$

Also,

$T=\frac{mg}{\cos \theta }$

$\therefore$ From the given options, we can conclude that, option (c) is the correct answer.