Question

Suppose I have an infinite plane of charge surrounded by air. What is the maximum charge density that can be placed on the surface of the plane before dielectric breakdown of the surrounding air occurs

Answer 1

Answer:

$53.1\mu C/m^2$

Explanation:

We are given that

Electric field,E=$3\times 10^6V/m$

We have to find the value of maximum charge density that can be placed on the surface of the plane before dielectric breakdown of the surrounding air occurs.

We know that

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

Where $\epsilon_0=8.85\times 10^{-12}$

Using the formula

$3\times 10^6=\frac{\sigma}{2\times 8.85\times 10^{-12}}$

$\sigma=3\times 10^6\times 2\times 8.85\times 10^{-12}$

$\sigma=5.31\times 10^{-5}C/m^2$

$\sigma=53.1\times 10^{-6}C/m^2=53.1\mu C/m^2$

$1\mu C=10^{-6} C$