Charge on a particle above a seemingly infinite charge plane

[Amay]

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

 

[hutchphd]

Your method is fine but the unit of mass in MKS (SI) is kg, so check your units again and make sure all is copacetic...

 

[Amay]

Your method is fine but the unit of mass in MKS (SI) is kg, so check your units again and make sure all is copacetic...

Ah, yes, Thank you very much.