Question

An electric field is established by applying a potential difference to the plates. it is found that a field of strength e0 will cause the droplet to be suspended motionless. write an expression for the droplet's charge q. let g be the acceleration due to gravity.

Answer 1

When the particle is suspended motionless its weight is in equilibrium with the force applied on through the electric field. Thus 
$mg=qE$
From this equality we can deduce the charge of the droplet necessary for the particle to stay suspended:
$q= mg/E$
where m is its mass and E is the electric field that is applied.