Question

a small charged ball is hovering in the state of equilibrium at a height h over a large horizontaluniformly charged dielectric plate

Answer 1

Given:

A small charged ball is hovering in the state of equilibrium at a height h over a large horizontaluniformly charged dielectric plate.

To find:

Charge on the ball.

Calculation:

Since the ball is in translational equilibrium we can say that the weight of the ball is being balanced by the electrostatic force experienced by the ball.

Let surface charge density of plates be $\sigma$

Net field intensity at height h ;

$E= \dfrac{ \sigma}{ \epsilon_{0}}$

So, as per FBD of object ;

$\therefore \: F_{E} = F_{g}$

$= > E \times q= m \times g$

$= > \dfrac{ \sigma}{ \epsilon_{0} } \times q= m \times g$

$= > q= \dfrac{mg \epsilon_{0}}{ \sigma}$

So, final answer is:

$\boxed{ \sf{ \red{ q= \dfrac{mg \epsilon_{0}}{ \sigma}}}}$