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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.