Download CHAPTER 15

A. Manalaysay – PHY2054, Fall 2004
CHAPTER 15
First, Coulomb’s Law applies to the force between two point charges:
tells magnitude only! The direction is determined by the system. Force
lies along the line connecting two charges. Opposite charges attract; like charges repel.
Electric Field: --A charge that feels an electric force due to other charges is said to be in
the presence of an electric field, E, defined as the ratio of the force to the value of the
charge:
F = q E --> The force a charged particle feels when placed in an external electric field.
Notice that charge, q, is a scalar, so F and E (which are vectors) must be either point in
the same direction or point in opposite directions. When would they point in opposite
directions?
Clearly, since charges produce forces on one another, and charges feel a force when they
are in an electric field, then charges themselves produce electric fields. If you look at
Coulomb’s Law long enough, you’ll see that:
Again, this tells the magnitude only. To find the direction, remember that
electric field points away from positive charges and towards negative charges.
------------------------------Gauss’s Law: In order to discuss Gauss’s Law we must talk about flux.
Flux is basically tells you how many electric field lines are passing through a surface.
But it depends on the orientation of things (i.e. angles and stuff). Here’s an analogy:
Imagine you stand next to a river and dip a vertical hula hoop into the water. You start
with the hula hoop perpendicular to the direction that the water is flowing. Flux would
be a measure of how much water is flowing through the hula hoop. Now if you rotated
your hula hoop about its diameter so that it is parallel to the direction the water is
flowing, no water actually goes through the hula hoop anymore. This is why the angle
matters. Without further ado, here’s the formula:
Flux:
KNOW WHAT THESE SYMBOLS MEAN! “ ” is flux (obviously).
“E” is the magnitude of the electric field at the surface, “A” is the area of the surface and
“theta” is the angle between the electric field and the normal to the surface (this is what
people mess up the most). A normal vector is simply the vector that is perpendicular to
the surface.
Gauss said: Let’s talk about a closed surface (e.g. a balloon, a cardboard box, etc.). The
things that go into calculating the flux through that surface might be complicated (i.e.
electric fields and angles), but the total flux out of the surface depends only on the
amount of charge inside that surface, in this manner:
--> Qenc is total enclosed charge. This applies to closed surfaces only.