# Floating speck of dust with charge

1. Sep 24, 2008

### roz77

So this is a problem my friend was doing. I don't remember the specific values for the variables, but it should be ok. There is a speck of dust floating above an infinite plane. The speck of dust has a charge q1. The plane has a charge density of sigma= xC/m^2. What is the mass of the speck of dust?

So we talked about it. We assumed that since the speck of dust is floating, the gravitational force downward should equal the electrostatic force that was repelling the dust. So we tried setting kq1q2/r^2 equal to mg, but there is no distance given. We weren't really sure how to proceed, and that's as far as we got. My friend has a test on this stuff tomorrow night, so im tryin to help him out.

Thanks.

2. Sep 24, 2008

### Irid

The formula you used only applies to two point charges. In the case of infinite plane, the electrostatic repulsion force is

$$F = \frac{q_1 \sigma}{2\epsilon_0}$$

independent of any distance. The rest of discussion about the gravitational force is correct.