Review of Basic Electrostatics

Part 1

When a piece of wire is connected between two terminals of a battery, electric current flows from the positive to the negative terminal. That is, the positive charges move from the region of higher potential to the region of lower potential. A simpler situation is shown below in which a positive charge q is repelled by another positive charge Q.

The electric force between the two charges is given by Coulomb's Law

(1)

in which r is a radial unit vector, and K is a proportionality constant which depends on the system of units we choose.

We visualize this in two steps. First, the charge Q creates an electric field E everywhere around it. The other charge, q, is acted upon by an electric force via the electric field at its location

(2)

Note that the above equation defines the electric field E as the force on a positive unit charge. Comparing the two equations, we see that

(3)

When a point charge Q creates an electric field everywhere as given by (3), an external agent has to perform a certain amount of work to move a unit charge from infinity to a point in space.

The potential at a point, V(r) is defined by

(4)

Equation (4) defines the electric potential at a point as the amount of work an external agent does to bring a positive unit charge against the field [notice the -E factor in equation (4)] from infinity to that point.

In this image, a motor does positive work pulling a positive charge into a region of higher potential. The motor is an external agent.

Go on to the Second Part of the Review. You may also wish to examine some applications of what you have just learned.


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