Question

Near the earth's surface, the electric field in the open air has magnitude 150 N/c and is directed down towards the ground. If this is regarded as being due to a large sheet of charge lying on the earth's surface, calculate the charge per unit area in the, what is the sign of the charge?

Answer 1

Hi there!

Using the equation for the electric field produced by an infinite sheet of charge:

$E = \frac{\sigma}{2\epsilon_0}$

E = Electric field strength (150 N/C)

σ = Surface charge density (? C/m²)

ε₀ = Permittivity of free space (8.8542× 10⁻¹² C²/Nm²)

We can rearrange the equation to solve for the surface charge density (charge per unit area)

$E = \frac{\sigma}{2\epsilon_0}\\\\\sigma = 2E\epsilon_0\\\\\sigma = 2(150)(8.8542*10^{-12}) = \boxed{2.656 \times 10^{-9} \frac{C}{m^2}}$