Floating speck of dust with charge

[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 I am tryin to help him out.

Thanks.

 

[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.

 

[baba89]

I would suggest using the equation F = qE, where F is the electrostatic force, q is the charge of the speck of dust, and E is the electric field created by the charged plane. Since the speck of dust is floating, the electrostatic force must be equal to the gravitational force, as you and your friend correctly assumed. Therefore, we can set F = qE = mg, where m is the mass of the speck of dust and g is the acceleration due to gravity.

To find the electric field, we can use the formula E = sigma/2*epsilon, where sigma is the charge density of the plane and epsilon is the permittivity of the medium (in this case, air). Then, we can substitute this into our equation and solve for m:

q(sigma/2*epsilon) = mg
m = q(sigma/2*epsilon)/g

Without knowing the specific values for q and sigma, it is not possible to calculate the mass of the speck of dust. However, this equation can be used to find the mass if the values are known. Additionally, it is important to note that this is an idealized scenario and in reality, there may be other factors at play that could affect the mass of the speck of dust. I wish your friend the best of luck on their test.