Electric field outside a conductor and its surface charge

In summary, the boundary condition for the electric field ##E## is ##E_{above}-E_{below}=\frac{\sigma}{\epsilon_0}\hat{n}## when considering a surface charge ##\sigma##. However, the field inside a conductor is zero, meaning that the field immediately outside the conductor is ##E=\frac{\sigma}{\epsilon_0}\hat{n}##. This differs from the field of a fixed plane of charge, as the field of a charged sheet of conducting material is not the same.
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Imagine a surface charge ##\sigma##. The boundary condition on ##E## is

##E_{above}-E_{below}=\frac{\sigma}{\epsilon_0}\hat{n}##, where ##\hat{n}## points outwards perpendicularly to the surface.

Because the field inside a conductor is zero, it requires that the field immediately outside is ##E=\frac{\sigma}{\epsilon_0}\hat{n}##.

But if the conductor is a large, flat plane with a uniform surface charge ##\sigma##, shouldn't the field be ##E=\frac{\sigma}{2\epsilon_0}\hat{n}##?
 
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What is an electric field outside a conductor?

An electric field is a region in space where an electric charge experiences a force. In the case of a conductor, the electric field is the force per unit charge on a test charge placed outside the conductor.

Why is the electric field outside a conductor zero?

According to Gauss's law, the net electric field outside a conductor is always zero. This is because any excess charge on the surface of the conductor creates an electric field that is equal and opposite to the external electric field, resulting in a net zero field outside the conductor.

What is the surface charge on a conductor?

The surface charge on a conductor is the net charge accumulated on its surface due to the redistribution of charges in response to an external electric field. This charge is concentrated on the surface of the conductor and is responsible for the zero electric field outside the conductor.

How does the shape of a conductor affect the surface charge and electric field?

The surface charge and electric field on a conductor's surface depend on its shape. If the conductor has sharp edges or points, the surface charge density will be higher, and the electric field will be stronger. In contrast, a smooth and round shape will result in a lower surface charge and weaker electric field.

Can the surface charge on a conductor be changed?

Yes, the surface charge on a conductor can be changed by manipulating the charges on its surface. This can be done by applying an external electric field or by connecting the conductor to a different charge source. The surface charge will redistribute to achieve a new equilibrium, resulting in a change in the electric field outside the conductor.

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