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Introduction to Electric Potential

Brief Review:


First class:

Two types of charge:
negative positive
electrons protons
ions w/ extra e- ions w/ deficit of e-

Coulomb's law:


Second class:

The electric field from a point charge Q is:

Superposition for collection of N point charges requires vector addition:


Next Week:

Next week we begin to explore application of calculus to determine E from a continuous distribution of charge:


where:

And then on to Gauss's law!

Today's Class:

All of the above methods for dealing with electrostatic interactions via E involve vector operations. Often it is easier (though not always) to consider another field, the electric potential. Represented by the symbol V, this field is scalar and thus has "easy" superposition algebra. Of course V is directly related to E as we will soon see!

The electric potential difference between two points A and B in an electric field is defined as the work that must be done per unit charge in moving the charge from A to B.

To the chalkboard for presentation of
Definition of potential Formula to find V from E
Potential of a point charge Potential of a point charge

Concept Check

Unit of potential is a joule/coulomb, called a volt. Unfortutately this unit is given the symbol V which is the same as the symbol used by HRW for electric potential, although they do use a slightly different font. (Some texts use the symbol lower-case phi for electric potential.)

Graphical Representation of the Electric Field:

Just as we described the electric field around a charged object by field lines, we may also describe the electric potential pictorially with equipotential surfaces (contour plots), where each surface corresponds to different fixed value of potential. Note: no work is required to move a test charge along an equipotential surface. This means that E is everywhere normal (perpendicular) to equipotential surfaces. (Otherwise work would be done!)

COMPUTER DEMONSTRATION: The computer program EM Field from Academic Physics Software will permit us to examine the equipotential surfaces that result from groups of point charges. First consider a single point charge of +4 units to get a feel for this capability of the program, plotting equipotential surfaces differing by 0.5 V. Then we examine relationship of field vectors to each contour, then field lines, finally noting the relationship of E to the gradient of V. Then we return to the study of pairs of point charges; first -4 and +4 units (forming a dipole), and then +4 and +4 units.


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Last updated Feb. 16, 1998.
Copyright George Watson, Univ. of Delaware, 1997.