PHYS208 9/8 Class
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Introduction to Electric Potential
Two types of charge:
|ions w/ extra e-
||ions w/ deficit of e-
The electric field from a point charge Q is:
for collection of N point charges
requires vector addition:
Next week we begin to explore application of calculus to determine
E from a continuous distribution of charge:
And then on to Gauss's law!
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 V and potential of a point charge.
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!)
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.
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 Sept. 8, 1997.
Copyright George Watson, Univ. of Delaware, 1997.