Question

A flat, wide cloud floats horizontally a few kilometers above the surface of Earth. Its lower surface carries a uniform surface charge density of -2.6×10-4 C/m2 , while there is no excess charge elsewhere in the cloud. What is the magnitude of the electric field, in newtons per coulomb, a few meters below the cloud, under the clouds approximate center, due to the charge distribution?

Answer 1

Magnitude of the electric field is $1.47\cdot 10^7 N/C$

Explanation:

In this problem, the length of the cloud (horizontally) is a few kilometers, while here we want to evaluate the electric field it produces just a few meters below the cloud.

Therefore, we can approximate the cloud as being an infinite sheet with charge on it.

The electric field produced by an infinite sheet of charge is perpendicular to the sheet and it is given by

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

where

$\sigma$ is the surface charge density

$\epsilon_0 = 8.85\cdot 10^{-12} F/m$ is the vacuum permittivity

For the cloud, we have

$\sigma=-2.6\cdot 10^{-4} C/m^2$

Therefore, the electric field produced by the cloud is

$E=\frac{-2.6\cdot 10^{-4}}{2(8.85\cdot 10^{-12})}=-1.47\cdot 10^7 N/C$

Where the negative sign means the field points towards the cloud.

Therefore, the magnitude of the field is

$1.47\cdot 10^7 N/C$

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