Conductors

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Conductors

We consider what happens when a material is placed inside an electric field.

Ideal Conductor

Properties

  1. There are "free", weakly bound electrons that are stripped off and free to move when an external E-field is applied
  2. These electrons move without resistance (i.e the conductor has resistance )
  3. There are infinite electrons available
  4. These electrons do not leave the conductor (they may go to the surface)

We can picture a conductor as having the positive charges (protons) nailed in place, with the negative charges (electrons) free to move. In the absence of an external E-field, the electrons would stick with the protons.

Conductors Inside Electric Fields

Rule 1: Electric Field Inside a Conductor is Always 0

Figure

In the figure above, the red E-field is created by some external charge, causing the electrons to move towards it on the surface. Due to the electrons moving to the left, the right side has a net positive charge. This creates an induced E-field inside the conductor, which cancels out the external E-field, leaving the net E-field inside 0 (i.e )

Rule 2: Conductors are Equipotential

(see equipotential)

Since inside the conductors is 0, if you walk from any point A to point B, the potential difference will also be 0.

For example, we do not consider voltage drops within a wire.

Rule 3: Charges will be Induced on the Surface of the Conductor

In the presence of an E-field, charge will be induced on the surface. Electrons will collect on the surface where the E-field is incident on the conductor boundary and positive charges on the other side.

Rule 4: There is no Induced Charge in the Volume of a Conductor

All the induced charge has to move to the surface of the conductors. There cannot be an induced charge in the volume of the conductor.

Using Gauss's law , if we draw a Gaussian surface that only encloses some of the charges, there will be a charge present, indicating there must be an electric field. This would contradict rule 1.

Rule 5: Any External E-field Lines Must be Perpendicular to the Conductor Surface

That is, there cannot be a tangential component to the field lines.

Rule 6: External E-field in a Cavity will be 0 (Faraday's Cage)

What happens if wee take a hollow conductor and put it in an E-field?

Figure

The E-field inside the hollow part is 0.

Faraday's Cage: By putting something inside a conductor box, we shield it from any external electric field.

This is why you don't get cancer from microwaves, your phone service doesn't work inside elevators, and why airplanes aren't fried by lightning.