Please help magnitude of the surface charge density question?

Question

In a laboratory experiment, an electron’s weight is just balanced by the force exerted on the

electron by an electric field. If the electric field is due to charges on two large, parallel, non-

conducting plates, oppositely charged and separated by 2.3 cm, what is the magnitude of the

surface charge density, assumed to be uniform, on the plates?

A. 2.3 × 10−20 C/m2 B. 2.3 × 10−22 C/m2 C. 4.9 × 10−20 C/m2 D. 4.9 × 10−22 C/m2

Answer 1

under balance > mg = qE

E = between 2 plates = ρ /eo = constant

ρ = sigma = charge/area = mg eo/q

1/4pi eo = 9*10^9

ρ = mg [4 pi eo/ 4pi q] = 9.1*10^-31*9.81/ [9*10^9 *4*3.14*1.6*10^-19]

ρ = 4.9*10^-22 C/m^2

option (D) is correct