Purpose

To gain some experience with equipotential lines and electric fields by experimentally determining the potential at various points between test charges and then drawing in the equipotential lines and the electric field lines.

Preliminary Discussion

The concept of a field surrounding the source of a force is a very important concept for all of physics. For this experiment, it is intended that you gain some experience with electric fields, study some of their effects, and make some measurements of the strengths of their sources.

You have already worked with one example of a vector field, the gravitational field (g). With every point in space near the earth we have associated a gravitational field vector g, which is the gravitational acceleration that a test body placed at that point and released, would experience. If m is the mass of the body and F the gravitational force ("weight") acting on it, g is given by

g = F/m [Newton/kg] · · · · · · (1.1)

This kind of field surrounds all objects with mass and can be detected using other objects with mass.

Similarly, the space surrounding an electrically charged object (i.e., an object with an excess electrical charge) is affected by the object, and we speak of an electric field in this space. The electric field vector (E) is defined operationally by placing a small test body carrying a test charge q_o (by convention assumed positive) at the point in space that is to be examined. When we measure the electrical force F that acts on this body, the electrical field E at the point is defined as:

E = F/q_o [Newton/Coulomb] · · · · (1.2)

The difference in the potential energy of any point B from that of any point A in an electric field is equal to the work W, required to transport a unit positive charge, q_o from A to B. W can be expressed using a quantity V and q_o, i.e., W = Vq_o, where V is simply the energy per unit charge, or V = W/q_o. This quantity is called the electric potential. It is measured in Joule/Coulomb = volt. The electric potential is a scalar.

An equipotential surface, or contour of constant potential, is simply the locus of all points which are at the same potential. Thus, the work required to convey a unit positive charge from any point in one such surface to any point in another is equal to the difference in the potential energies of the two surfaces, or equal numerically to the difference in potential of the two surfaces. It is evident, then, that an equipotential surface is further characterized by the fact that a charge may be constrained to move between any two points in the same surface without any work having been expended. The above is equivalent to stating that the field strength or intensity is always oriented in a direction which is perpendicular to the equipotential surfaces, since in order that work be done under the action of the field, at least a portion of the motion of the charge must be in the direction of the force.

Apparatus

Two conducting sheets will be available, one with its positive and negative electrodes in the form of two separated points, the other with its electrodes in the form of two separated parallel lines. The lines of force and the equipotential contours formed in the first case are geometrically identical to the lines and contours formed when the two electrodes are replaced by two unlike charges of equal magnitude. In the second case the lines and contours duplicate those of two parallel metal plates of equal and opposite charges.

Laboratory Experiment and Final Report

1. Set up the apparatus as shown in the figure. When the two probes are at the same potential, there will be no current flowing through the microammeter. Determine the equipotential lines between two oppositely charged points and draw a map of them to accurate scale on the cross-section paper. Draw in the lines of force showing direction of flow of the charges, i.e., the electric field lines. What direction will the charges always take with respect to the equipotential lines? Note: The voltmeter should be disconnected when you make your measurement.

2. Repeat for a second charge configuration.