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Reading Guide

The first part of Chap 6 is more theoretical about the connections between potential and electric field.

Essentially the electric field is the derivative over space of the potential while the potential is the integral of the electric field: Relations 26.3 and 26.9.

Since the electric field is a vector and potential is a scalar, the relationships are actually a line integral of E yields V while the gradient of V yields E. As the book states, we will mostly do this graphically.

• remember that you decide where the zero of potential is. For a point charge, choose the zero to be at infinity.
• there is a minus sign in both expressions.
• the E field points in direction of lower V, going down with equipotential surfaces. The E field is perpendicular to the equipotential surfaces.

Conductors.

Conductors are special compared to insulators because the charges can move and they will move as much as they can. Starting next week, we will start looking at situations where charges are moving inside of conductor leading to currents.

In week 4, we saw that in static equilibrium,

• the electric field is zero inside the conductor.
• the electric field at the surface of a conductor is perpendicular to the surface.

We now can add a few more observations with conductors regarding potential

• the whole conductor is an equipotential.
• the E field goes like V/R for a conductor tip of size R. The electric field can become very intense and create corona discharge.

In this demo video, I show the Wimhurst machine and Van Der Graff, I should have shown this video earlier in the course in the context of static electricity but it is relevant here with the Corona discharge effect.

The idea is that the electric field is very intense near the tip of the metal and one can discharge a Van Der Graaf.