# Behaviours of charges inside a conductor(slightly complex scenario?)

• negation
In summary, a spherical conductor in electrostatic equilibrium has no net electric field inside or on its surface. This is due to Gauss's law, which states that the integral of the electric field over a closed surface is equal to the charge enclosed divided by the permittivity of free space. This means that if there is no electric field inside the conductor, the enclosed charge must be zero. This is why excess charges on a conductor will always reside on the surface, even in more complex cases like a coaxial cable. If there were any regions with excess charges, the electrostatic equilibrium would be disrupted.
negation
A SPHERICAL conductor in electrostatic equilibrium has no further motion of charges within it. From this, it must imply that there is no net electric field in a conductor and this must necesssarily imply that qenclosed is zero.
This is fairly easy to see from Gauss's law:
(closed)∫E.dA = qenclosed0
If E = 0, then ε0 = 0
Assuming inside the conductor is a negative point charge, then eventual distribution will result in negative charges on the inner surface of the conductor and positive charges on the outer surface of the conductor.

However,

1) It is hard for me to see this visually in a more complex case such as a coaxial cable.
2) Why is the electric field outside the SPHERICAL conductor ≠ 0 for a point outside of the conductor? If 2 oppiste charge cancels themselve at the boundary of the surface, why does there exists electric field outside the conductor?
3) Why must excess charge reside on the surface of a conductor? What if, in the case of a coaxial cable, there are multiple layers of conductor?

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3) if there were any regions in the conductor with excess charges, a Gaussian surface around that region would have non-vanishing electric field creating an electric current contradicting the electrostatic equilibrium hypothesis

## 1. How do charges behave inside a conductor?

Inside a conductor, charges are free to move around due to the presence of loosely bound electrons. This allows them to flow easily in response to an electric field.

## 2. What happens to charges when a conductor is placed in an electric field?

When a conductor is placed in an electric field, charges will redistribute themselves in order to cancel out the effects of the field. This results in a build-up of charges on the surface of the conductor.

## 3. How does the shape of a conductor affect the distribution of charges inside?

The shape of a conductor can affect the distribution of charges inside by influencing the electric field and the way charges are able to move. For example, sharp edges can result in a higher concentration of charges, while curved surfaces can result in a more evenly distributed charge.

## 4. What is the difference between a conductor and an insulator in terms of charge behavior?

A conductor allows charges to move freely, while an insulator does not. In an insulator, charges are tightly bound to their atoms and are not able to move easily in response to an electric field.

## 5. How does temperature affect the behavior of charges inside a conductor?

Temperature can affect the behavior of charges inside a conductor by influencing the speed at which the charges are able to move. As temperature increases, the vibrations of atoms in the conductor also increase, making it more difficult for charges to flow.

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