2. A Charged, Thin Sheet of Insulating Material + + + + + + + + + + +

3. 1) There is a conducting spherical shell, inner radius A and outer radius B. If you put a charge Q on it, find the charge density everywhere. 2) There is a conducting spherical shell, inner radius A and outer radius B. A charge Q is put at the center. If you put a charge Q 2 on the shell, find the charge density everywhere.

4. Electric field near a surface of a conductor a

5. d + + + + + + a - - - (the total field at any point between the plates) Two parallel conducting plates

6. An Apparent Contradiction + + + + + + - - -

7. + + + + + + - - - Near the surface of any conductor in electrostatics

8. What have we learned about conductors? There is no electric field inside a conductor Net charge can only reside on the surface of a conductor Any external electric field lines are perpendicular to the surface (there is no component of electric field that is tangent to the surface). The electric potential within a conductor is constant

12. since inside the conductor. For any two points and inside the conductor The conductor’s surface is an equipotential.

13. Equipotential Surfaces An equipotential surface is a surface on which the electric potential V is the same at every point. Because potential energy does not change as a test charge moves over an equipotential surface, the electric field can do no work on such a charge. So, electric field must be perpendicular to the surface at every point so that the electric force is always perpendicular to the displacement of a charge moving on the surface. Field lines and equipotential surfaces are always mutually perpendicular.

15. Method of images: What is a force on the point charge near a conducting plate? - - - - - - - - - - - - - Equipotential surface

16. The force acting on the positive charge is exactly the same as it would be with the negative image charge instead of the plate. The point charge feels a force towards the plate with a magnitude:

17. Method of images: A point charge near a conducting plane. - - - - - - - - - - - - - Equipotential surface