1. Electric Field Lines - a “map” of the strength of the electric field. The electric field is force per unit charge, so the field lines are sometimes called lines of force.

2. Electric field lines are always directed away from positive charges and toward negative charges. Where lines are closest together, the electric field is strongest.

3. Where the electric field lines are equally spaced, the electric field has the same strength at all points.

4. Two separated point charges that have the same magnitude but opposite signs are called an electric dipole.

5. The electric field of a dipole is proportional to the product of the magnitude of one of the charges and the distance between the charges. This product is called the dipole moment.

6. Electric field lines always begin on a positive charge and end on a negative charge and do not start or stop in midspace. Also, the number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.

7. Field lines never cross, because at any one point there is only one value for the electric field.

8. Excess electrons within a conductor are repelled by all electrons in the material. Due to the distance factor of Coulomb’s law, 1/r 2, they rush to the surface of the conductor.

9. They spread out evenly over the surface (They repel each other also). An excess positive charge also moves to the surface of a conductor.

10. At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor.

11. Free electrons within the conductor are not moving, so no electric field exists there. At equilibrium under electrostatic conditions, the electric field at any point within a conducting material is zero.

12. Additionally, the conductor shields any charge within it from electric fields created outside the conductor. Electronic circuits are often protected from “stray” electric fields by metal containers.

13. A conductor alters the electric field around it. The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions.

14. If the field were not perpendicular, there would be a component parallel to the surface which would make the free electrons move over the surface; but the electrons do not move, so the field must be perpendicular.

15. An electric field is sometimes produced by charges spread out over a region, not by a single point charge. An extended collection of charges is called a charge distribution.

16. Gauss’ law describes the relationship between a charge distribution and the electric field it produces. Gauss law for a point charge is: EA = q/ε 0

17. EA = q/ε 0 E is electric field magnitude A is the area of the surface q is the charge in coulombs ε 0 is the permittivity of free space

18. The product of electric field magnitude E and the area of the surface A, EA is called the electric flux,  E.  E = EA. This definition for flux only works for a point charge and a spherical Gaussian surface.

19. The Gaussian surface can have any arbitrary shape, but it must be closed. The field direction is not necessarily perpendicular to the surface.

20. The magnitude of the electric field need not be constant on the surface, it can vary from point to point.

21. By dividing the surface into many small sections, finding the flux for each section, and adding them together, the total flux of the surface can be found.  E = ∑(E cos  )∆A

22. Gauss’ law relates the electric flux  E to the net charge q enclosed by the arbitrarily shaped Gaussian surface.

23. Gauss’ law The electric flux through a Gaussian surface is equal to the net charge q enclosed by the surface divided by the ε 0, the permittivity of free space:  E = ∑(E cos  )∆A = q/ε 0. The SI unit of electric flux: Nm 2 /C

24. Ex. 14 - A thin spherical shell has radius R. A positive charge Q is spread uniformly over the shell. Find the magnitude of the electric field at any point (a) outside the shell and (b) inside the shell.

25. Ex. 15 - Use Gauss’ law to prove that the electric field inside a parallel plate capacitor is constant and has a magnitude E =  /ε 0.  is the charge density on a plate.