What are the strength and direction of an electric field that will balance the weight of a 0.9 g plastic sphere that has been charged to -3.4 nc?

(a) The force exerted by the electric field on the plastic sphere is equal to

where  is the charge of the sphere and E is the strength of the electric field. This force should balance the weight of the sphere:

where m is the mass of the sphere and g is the gravitational acceleration.

Since the two forces must be equal, we have:

and so we find the intensity of the electric field


(b) Now let's find the direction of the field. The electric force must balance the weight of the sphere, which is directed downward, so the electric force should be directed upward. Since the charge is negative, the force is opposite to the electric field direction, and so the direction of the electric field is downward.