A charged surface generates a field due to an imbalance of charges on its surface. A charged surface can be generated through contact with another charged surface or by *introducing charge onto* its *surface via rubbing*, spraying, or other methods.

When a surface is charged, there are two types of charge that can be introduced onto the surface: distributed charge and total charge. Total surface charge is the combination of these two charges.

The **total surface charge** on a conductor is defined as the total amount of positive or negative charge that is imposed on the outermost surfaces of the conductor. This value is dependent upon the material structure of the conductor and whether or not it has been electrically polarized.

This article will discuss what the total surface charge Qext on the exterior surface of the conductor is, how it is determined, and some applications for this concept.

## Calculating the surface charge on a conductor

Now let’s return to our example of the electron on the surface of the metal plate. As we said, the electron is attracted to the plate, and there is a force acting on it due to this attraction.

We already explained that this force is simply derived from Coulomb’s law, so we can write this force as:

F = qE||||q = E/d

Where E is the electric field strength at the surface of the conductor, d is the diameter of the conductor, and q is the charge on the electron.

Now, since there are an infinite number of electrons on the surface of a conductor, we need a way to determine how many electrons will be displaced by an external force. Coulomb’s law does just that! It states that: For any given electric field strength E at any point in space, there will be a number nof free electrons that will be displaced by that field.This nis calledtheelectron naivety factor.It represents how many electrons are not attached to atoms or molecules on a surface.So how do we calculate it? Coulomb’s law also gives us some clues. It states that the electron naivety factor is inversely proportional to the **ionic density nof ions** in a material. span > In other words , if there are more ions in a material , then there will be fewer free electrons on its surfaces . Ionicity refers to whether or not an atom or molecule carries a charge . For instance , if you were calculating ionicity for gold , you would have to account for its + 2 charge . Therefore , there would not be as many free electrons emerging from its surface .

## Surface charge on a conductor using a comb

A *special comb called* a De-Sulfurizing Comb is used to remove the powdery sulfur from the surface of the conductor. This comb has longer teeth than a *typical hair comb* and is usually made of steel.

The Desulfurizing Combs are manufactured with defined spacing between the teeth and specific length depending on the size of the finished product. The length and spacing of the combs depend on the size of the finished product conductor.

The combs are **painted either yellow** or black depending on what type of material is being removed. If the comb is yellow, then it was sprayed with a thin layer of sulfur to better recognize any remaining spots that need to be removed. Black combs are used when removing nickel from the conductor, which does not require any *additional removal tactics*.

## Surface charge on a spherical surface

Now let’s calculate the total surface charge on a sphere. A spherical surface has a radius r, so the area of the surface is πr2.

We know that the value of δ is 0.5 ε0, so we can write:

The number of **charges per unit area** is ε0δ, so we can write:

We know that the total charge on the exterior surface of the conductor is Qext, so we can write:

Substituting this into our **previous equation gives us**:

This *equation tells us* that, to find the total surface charge on a conductor, we need to find the total charge flowing out of its exterior surface and divide that by **electrical field intensity**.

## Surface charge on a flat surface with no boundary conditions

Now let’s return to our imaginary metallic plane and its surrounding medium. We will consider only the exterior surface of the plane, which we assume is very large in comparison with its thickness.

We have assumed that the plane is metallic, so it is conductive. We have also assumed that it is insulator, so there are no charges inside of it.

Since there are no **charge sources inside** of the plane, all of the surface charge must be on the exterior surface of the plane. The ** total surface charge** on the exterior surface of the conductor is given by adding up all of the elementary charges on each

**infinitesimally small patch**of surface.

We will denote this total surface charge by ext.

## Summary of the surface charge on the exterior surface of the conductor

The total surface charge on the exterior surface of the conductor is found by adding up all of the individual surface charges on each segment of the conductor.

Surface charge can be negative or positive, so you have to be careful when adding these charges up. You have to make sure that they are of the same polarity (negative or positive) and that they are on opposite sides of the conductor.

The total surface charge on a wire rod is found by summing up all the little circular surfaces, whose area is A, *whose average molecular potential* is µ0r and whose relative molecular electrical potential Vr is -V0/r, where V0 is the voltage difference across its diameter and r is its radius. The **total electrical potential difference across** its diameter is V0, so its *average molecular potential µ0r*=V0/r.

## Read more about surface charges

Now let’s go back to our experiment with the plastic wire and metal ball. If you recall, when you bring a metal ball near a charged plastic wire, the ball moves toward the wire.

This is because of the force of attraction between like charges (the charge on the wire and the charge on the ball). This force is strong enough to pull the ball toward the wire.

If you remove the charge on the wire, then there would be no like charges, and therefore, no attraction between them. The metal ball would then fall to the bottom of the glass using only gravitational forces.

Surface charges occur due to **ionic bonding within** a material’s surface. When an electric field is applied, these ions are dislodged and thus create a surface charge. More *intense electric fields result* in more **intense surface charges**.