Experiment 4
ELECTRIC FIELDS AND ELECTRIC POTENTIAL

PRELAB

PURPOSE

To investigate the electric field and potential field around simple source configurations, and to understand the relationship between them.

EQUIPMENT   graphite paper with electrode contacts, DataPro interface with voltage probes, voltmeter, 5 volt dc supply, knife switch, half meter stick.

RELEVANT EQUATIONS

 Electric Field Electric Potential Field-Potential Relationship

DISCUSSION

A. The Electric Field

The electric field E is a measure of the electric force per unit charge that a given arrangement of charges (the field source) exerts on a tiny positive test charge in the vicinity (tiny because it should be so small that the test charge itself does not affect the result). It is therefore a vector quantity because the electric force as defined above has both direction and magnitude. This relationship can be expressed as:

 (1)

The electric field is a quantity which can be defined throughout all space for a given source distribution. A good example is the electric field produced by a single point charge. The field lines are illustrated in Fig. 4-1.

Figure 4-1: The Electric Field Surrounding a Positive and a Negative Charge

The direction of the electric field is indicated by the arrows. Notice that the direction of E at a given point in space is always the same as what the direction of the electric force would be on a positive charge if it were located there. What isn't so apparent from the field diagram is that the relative strength of the field is indicated by the density of spacing of the lines. Thus the force on a positive test charge gets weaker as the charge is moved farther away from the point charge source. The common unit of measure for the electric field is volts/meter.

An important property of the electric field is the fact that the resultant field produced by more than one source charge is simply the vector sum of the fields produced by each individual charge at the location of interest. There exist for example, multi-charge source configurations where the electric field remains constant throughout a given region of space. In this experiment you will investigate the electric field produced by two different source arrangements.

B. Electric Potential

Another quantity that is often an important consideration when dealing with charge arrangements is the energy associated with the configuration. Once again, it is convenient to take a tiny positive test charge and determine how much potential energy it has at a given location.

The electric potential at a given point in space is defined to be the potential energy per unit charge possessed by the test charge due to the presence of the source charge(s). This relationship can be expressed as:

 (2)

We note that the electric potential is a quantity that has magnitude only-- there is no direction associated with it. It is therefore what is often referred to as a scalar quantity. Because of its importance in electrical work, the potential has a specific unit associated with it-- the volt. For a specific charge distribution, points where the electric potential is the same are especially useful to know. In three dimensions these points define surfaces called equipotentials, but in a two-dimensional plot, they become lines. In Fig. 4-2, several equipotential lines are shown drawn in for case of the point charge source. The electric field lines have also been plotted on the same diagram in order to illustrate a very important property of the equipotential lines (surfaces)-- they are always perpendicular to the electric field at any point. The magnitude of the electric field at a point is proportional to the difference in potential ΔV, evaluated over a very small distance Δx in the field direction, divided by that distance:

 (3)

Figure 4-2: Equipotentials Surrounding a Positive Point Charge

In the procedures that follow you will determine the equipotential lines along with the field lines for each source distribution, as well as the relationship between the two.

Print out and complete the Prelab questions.