Question

A parallel-plate capacitor is constructed of two horizontal 17.2-cm-diameter circular plates. A 1.1 g plastic bead with a charge of -8.0 nC is suspended between the two plates by the force of the electric field between them. What is the charge on the positive plate?

Answer 1

The radius of the plates is r = 17.2/2 = 8.6 cm = 0.086 m

The area of one plate is

Let Q be charge on the positive plate, the surface charge density of the positive plate is

Assuming that the charge are very large, the electric field between two large charge parallel plates is

The magnitude of electric force on charge q is

The other force acting on the bead is the gravitational force of Earth mg.

To suspend the negatively charged bead on in between the plates, the negatively charged plate should be parallel to the ground and below the bead, while the positively charged plate should be above the bead. The free body diagram of the bead in this condition is shown below:

The charge on the bead is negative, so the positive charged plate attract the bead while negative charge plate repel the bead. The force on the bead of both the plates points in the up direction.

In equilibrium the electric force will balance the gravitational force of the Earth.

Substituting , , we get

or