Question

A proton starts from rest near the surface of a sheet of charge. It experiences a force of 14.0 microNewtons towards the sheet. What is the surface charge density of the sheet? (Ignore the gravitational force on the proton.)

Answer 1

The surface charge density of the sheet is 1547.516 C/m²

Step-by-step explanation:

Given;

force experienced by the proton, F = 14.0 μN

Electric field near an infinite sheet with surface charge density (σ) is given as;

E = σ/2ε₀

The force of attraction the proton experienced towards the sheet;

F = Eq

F = q(σ/2ε₀)
`= (q \sigma)/(2 \epsilon_o)`

where;

q is the charge of the proton

σ is the surface charge density of the sheet

ε₀ is the permittivity of free space

`F = (q \sigma)/(2 \epsilon_o) \\\\\sigma = (2F \epsilon_o)/(q) \\\\\sigma = (2*14*10^(-6)*8.854*10^(-12))/(1.602*10^(-19)) = 1547.516 \ C/m^2`

Therefore, the surface charge density of the sheet is 1547.516 C/m²