Surface charge density of a conducting spherical shell

[Samanko]

The textbook says
' A conducting sphere shell with radius R is charged until the magnitude of the electric field just outside its surface is E. Then the surface charge density is σ = ϵ0 * E. '

The textbook does show why. Can anybody explain for me?

 

[Delta2]

Is this homework?

In any case apply Gauss's law with gaussian surface a sphere that has the same center as the charged sphere and radius $R+dr$ where $dr$ infinitesimal. You should get as result an equation that relates E (the electric field at distance R+dr) and $\sigma$ and $R+dr$. Take the limit of that equation as $dr\to 0$ and you end up with the equation displayed in your textbook.

 

[alan123hk]

Equation σ = ϵ0 * E applies to conductive surfaces, regardless of their shapes

 

[Samanko]

Is this homework?

In any case apply Gauss's law with gaussian surface a sphere that has the same center as the charged sphere and radius $R+dr$ where $dr$ infinitesimal. You should get as result an equation that relates E (the electric field at distance R+dr) and $\sigma$ and $R+dr$. Take the limit of that equation as $dr\to 0$ and you end up with the equation displayed in your textbook.

Got it! Thanks.