Question

A tiny ball (mass = 0.010 kg) carries a charge of -24C. What is the electric field magnitude that would cause the ball to float above the ground?

Answer 1

Use the relation between electric force and electric field and the concept of gravitational force to calculcate the electric field.  The electric force is given by

$F_e = qE$

And the gravitational force is

$F_g = mg$

For the ball to float above the ground, the magnitude of electric force on the ball must be equal to the magnitude of the gravitational force. That is must be a equilibrium condition, so,

$F_e = F_g$

$qE = mg$

$E = \frac{mg}{q}$

Replacing the values we have that,

$E = \frac{(0.010)(9.8)}{-24*10^{-6}}$

$E = -4.083*10^{3} N/C$

Therefore the electric field magnitude that would cause the ball to float above the ground is $-4.083*10^{3} N/C$