ENERGY OF A CHARGE IN AN ELECTRIC FIELD

1. Introducing the concept of "work"

The mechanical concept of WORK is discussed in Grade 12. For the purpose of this topic however, it is necessary that we define it in terms of two quantitities with which you are already familiar, namely FORCE and DISTANCE. Work, W, is done on an object if a force, F, acts on that object for a distance, Δx. Then

Work is measured in the same units as energy, namely, the JOULE, J.

2. The field between two parallel charged plates

The field lines between two large, flat, parallel, oppositely charged conducting plates are perpendicular to the plates:

As long as we stay AWAY FROM THE EDGES, the field will be UNIFORM (homogeneous). Near the edges the field becomes INHOMOGENEOUS and the field strength DECREASES.

3. The potential energy of a charged particle in a field

A charged particle in an electric field will have an electrical potential energy, just as a mass will have a gravitational potential energy in a gravitational field:

Gravitation       Electricity
     
A mass m is placed in a gravitational field g N·kg-1, a distance h above the ground. Its gravitational potential energy is
mgh joules (kg·N·kg-1·m = N·m).
      A positive charge q is placed in a uniform electric field E set up between two charged parallel plates. If the particle is at a distance s from the negative plate, its electrical potential energy is qEs joules (C·N·C-1·m = N.m)

Just as a mass will accelerate in a gravitational field, thereby gaining kinetic energy and losing potential energy in the process, a charge will accelerate in an electric field and kinetic energy at the expense of its potential energy.

4. Work done on a charged particle in a field

A set of charged parallel plates may be considered as a device that produces an electric field. As long as the field is uniform, it is easy to calculate the work done by the field, E, on a charged particle with a charge Q.

The force on the charge Q will be given by the expression F = EQ. This force will cause the particle to accelerate in the field in the direction of the force (towards the negatively charged plate in the case shown above) if it is free to do so.

After the particle has moved a distance s, the work W done on it will be

Positive charges will accelerate in the direction of the field, while negative charges will accelerate in a direction opposite to that of the field.

When the particle accelerates, it will acquire KINETIC ENERGY (energy due to motion). By virtue of being located in an electric field, a charged particle has POTENTIAL ENERGY. The principle of conservation of energy dictates that the KINETIC ENERGY GAINED by the charged particle accelerating in the field is EQUAL TO ITS LOSS IN POTENTIAL ENERGY.

4. Potential difference

If the electric field is NOT UNIFORM, it is not so simple to calculate the energy change due to moving a charge in the field. It is therefore useful to define a quantity which describes the work done in moving unit charge from one point in the field to another point.

We call this quantity the POTENTIAL DIFFERENCE between the two points:

V is the symbol for potential difference, which has units of JOULES PER COULOMB, (J·C-1). As this is an important quantity, it is given its own unit, the VOLT, (V), in honour of Alessandro Volta, who invented the first workable battery.

"One volt is the potential difference between two points in an electric field such that one joule of work is done in moving one coulomb of charge from one point to another."

5. Potential at a point

Consider V, the potential difference between two points a and b situated in a uniform electric field E. It is incorrect to speak of the potential of one point without reference to another point. The point b is said to be at a higher potential than the point a if work is done AGAINST electric forces when a positive charge is moved from a to b. (Click here to see an animation). In this example, the electric field is from left to right, and the positive charge, initially at b moves AGAINST the field. Work has to be done on the charge in order to effect that motion.

It is however often convenient to consider the potential at a point, and this is permissible if a common reference point of zero potential is chosen. This point is taken to be an infinite distance away from the charge producing the field.

The potential at a point can be defined as the WORK REQUIRED TO MOVE ONE COULOMB OF CHARGE FROM INFINITY TO THAT POINT.

6. Electric field strength as a function of potential difference

It much easier to determine the electric field strength between parallel plates by measuring the potential difference between them than by measuring the force on a charge.

Let's do this by considering the work done, W, in moving a charge Q a distance d in a field E.

We know, from the definition of the potential difference V, that W = VQ (a)

But we may also write W = Fd =EQd (b)

Equating (a) and (b) gives EQd = VQ, or, E = V/d

In the case of parallel plates having a potential difference, V, separated by a distance, d, the field strength E is

The formula suggests that the units of E are VOLTS PER METER (V·m-1). These are identical to NEWTONS PER COULOMB, N·C-1, since



Find out about Millikan and his famous "Oil Drop Experiment"!

7. Additional questions