Question

A small plastic ball of mass m and having charge q is suspended by means of an insulating thread from a fixed point. There exists an electric field of magnitude E directed along horizontal. Acceleration due to gravity is g. What is the maximum angle by which the string gets deflected?​

Answer 1

Given:

A small plastic ball of mass m and having charge q is suspended by means of an insulating thread from a fixed point. There exists an electric field of magnitude E directed along horizontal. Acceleration due to gravity is g.

To find:

Max angle by which the string gets deflected?

Calculation:

Let the angle of the string with vertical be $\theta$.

Now, from the Free Body Diagram of the ball, we can say that the tension in the wire (T) can be broken down into components such as:

$1) \: T \cos( \theta) = mg \: \\ 2) \: T \sin( \theta) = Eq$

Dividing the 2 Equations, we get :

$\therefore \: \dfrac{T \sin( \theta) }{T \cos( \theta) } = \dfrac{Eq}{mg}$

$\implies \: \dfrac{ \sin( \theta) }{ \cos( \theta) } = \dfrac{Eq}{mg}$

$\implies \: \tan( \theta) = \dfrac{Eq}{mg}$

$\implies \: \theta = { \tan}^{ - 1} \bigg(\dfrac{Eq}{mg} \bigg)$

So, the final answer is:

$\boxed{ \bold{ \: \theta = { \tan}^{ - 1} \bigg(\dfrac{Eq}{mg} \bigg)}}$