Consider a horizontal, insulating plane that is uniformly and negatively charged

Question

Consider a horizontal, insulating plane that is uniformly and negatively charged. Assume the plane is very large and may be modeled as being infinite in extent. The magnitude of the electric field .100m from the place is 2.5x10^5 N/C.

What is the surface charge density of the plane?

A particle of mass 5.35x10^-6 kg is observed to be at rest 0.100m below the plane. Gravity acts downward in the figure, and the magnitude of the free-fall acceleration is 9.8m/s^2. What is the charge of the particle?

Explanation / Answer

electric field due to infinite sheet = sigma/ epsilon

2 .5x10^5N/C =sigma /epsilon

sigma= 2.5x10^5 * 8.85 *10^-12 =0.00000221 C/m2

mg =Eq

q=mg/E = 5.35x10^-6 *9.8 /  2 .5*10^5 =   2.92 *10-10 c

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