# Charge on a particle above a seemingly infinite charge plane

## Homework Statement:

A 2.0 m × 4.0 m flat carpet acquires a uniformly distributed charge of −10 μC after you and your friends walk across it several times. A 2.0 μg dust particle is suspended in midair just above the center of the carpet.

What is the charge on the dust particle?

## Relevant Equations:

F= ma
E= σ/2e0 (σ is the surface charge density and e0 is epsilon naught)
E= F/q
At first I take the uniformly distributed charge and then divide it by the area of the carpet to get the surface charge density σ

-10E-6 C / 8m^2 = σ = -1.25E-6C/m^2

Then I divide the surface charge density by 2e0 to get the electric field strength caused by the infinite plane

-1.25E-6/(2(8.85E-12 C^2/N.m^2 )) = -700621. N/C = E

Then I take the gravitational force on the particle

F = (2E-6)(9.81m/s^2) = 1.962E-5 N

Then I re arrange the formula of E=F/q to be have q on one side and then I substitute in numbers.

qE= F q= F/E

(1.962E-5 N) / (-700621N/C) = -2.778192 E-10 C or -2.8 E-10 C