A small glass bead has been charged to +19 nC. A metal ball bearing 1.0 cm above the bead feels a 0.030 N downward electric force. What is the charge on the ball bearing?

To find the charge on the ball bearing, we can use Coulomb's Law, which states that the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:

F = k * (q1 * q2) / r^2

Where:
F is the electric force,
k is the electrostatic constant (9 x 10^9 N m^2/C^2),
q1 and q2 are the charges on the two objects, and
r is the distance between them.

In this case, we are given:
q1 (charge on the glass bead) = +19 nC (nanoCoulombs),
F (electric force felt by the ball bearing) = 0.030 N,
r (distance between the glass bead and the ball bearing) = 1.0 cm = 0.01 m.

We rearrange the formula to solve for q2 (charge on the ball bearing):

q2 = (F * r^2) / (k * q1)

Substituting the given values:

q2 = (0.030 N * (0.01 m)^2) / ((9 x 10^9 N m^2/C^2) * (+19 x 10^-9 C))

Calculating this expression will give us the charge on the ball bearing.

It makes no difference what the materials are. Use Coulomb's law. The force depends only upon the charge and the separation. Since the electrical force is attractive, the charge on the ball bearing is negative (opposite to the glass charge.)

Note that the gravity force has already been subtracted.