# Surface charge density of a conducting spherical shell

• Samanko
In summary, the textbook explains that for a conducting sphere shell with radius R that is charged until the electric field just outside its surface is E, the surface charge density is given by σ = ϵ0 * E. To understand why, one can use Gauss's law with a gaussian surface of radius R+dr and take the limit as dr approaches 0. This will result in an equation relating E, σ, and R+dr, which simplifies to the equation in the textbook. This equation applies to conductive surfaces of any shape.
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?

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.

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

Samanko
Delta2 said:
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.

Delta2

## 1. What is surface charge density?

Surface charge density refers to the amount of electric charge per unit area on the surface of a charged object. It is typically denoted by the symbol σ and is measured in units of coulombs per square meter (C/m²).

## 2. How is surface charge density calculated for a conducting spherical shell?

The surface charge density of a conducting spherical shell can be calculated by dividing the total charge on the shell by the surface area of the shell. This can be expressed as σ = Q/4πr², where Q is the total charge and r is the radius of the shell.

## 3. What factors affect the surface charge density of a conducting spherical shell?

The surface charge density of a conducting spherical shell is affected by the amount of charge on the shell, the radius of the shell, and the dielectric constant of the surrounding medium. It is also influenced by the presence of any nearby charged objects.

## 4. How does the surface charge density of a conducting spherical shell impact its electric field?

The surface charge density of a conducting spherical shell is directly proportional to the electric field strength at the surface of the shell. This means that a higher surface charge density will result in a stronger electric field at the surface of the shell.

## 5. Can the surface charge density of a conducting spherical shell be negative?

Yes, the surface charge density of a conducting spherical shell can be negative. This means that there is a net negative charge on the surface of the shell, which can occur if there is an excess of electrons on the surface compared to protons.

• Electromagnetism
Replies
4
Views
190
• Electromagnetism
Replies
14
Views
2K
• Electromagnetism
Replies
24
Views
5K
• Electromagnetism
Replies
35
Views
2K
• Electromagnetism
Replies
3
Views
2K
• Electromagnetism
Replies
5
Views
1K
• Electromagnetism
Replies
13
Views
1K
• Electromagnetism
Replies
11
Views
1K
• Electromagnetism
Replies
2
Views
677
• Electromagnetism
Replies
8
Views
1K