# 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

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.)

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2 years 2021-07-27T15:56:11+00:00 1 Answers 14 views 0

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

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) $$= \frac{q \sigma}{2 \epsilon_o}$$

where;

q is the charge of the proton

σ is the surface charge density of the sheet

ε₀ is the permittivity of free space

$$F = \frac{q \sigma}{2 \epsilon_o} \\\\\sigma = \frac{2F \epsilon_o}{q} \\\\\sigma = \frac{2*14*10^{-6}*8.854*10^{-12}}{1.602*10^{-19}} = 1547.516 \ C/m^2$$

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