1. LESSON 25 Electric Potential áDefinition áComparison to Potential Energy áEquipotential Surfaces áElectric Potential due to point charge áElectric Potential due to many charge áElectric Potential Energy of Interaction

2. áon moving object from initial point to final point F Work done by a force F

3. r ds(r)=dx(r)i+dy(r)j+dz(r)k F(r)F(r) riri rfrf Line Integral

4. Potential Energy of the object  Work done by a conservative force on an object is equal to the negative of the change of Potential Energy of the object Kinetic Energy áThus equal to the change of Kinetic Energy of the object Potential Energy

5. Capacitor

6. Electric Potential

7. Potential Difference  The change of electrical P.E. per unit charge between an initial point and a final point is called the Potential Difference between the points áIt is the change of electric potential between the two points. Electric Potential Difference

8. zero áBy definition the P.E. at a point infinite distance from the source of a force is zero zero áThus the electric potential at a point infinite distance from the source of an electric field is zero Potentials at a point

9. Formula Electric Potential at point r

10. [U]/[Q] = J/C= V (Volts) S.I. Units

11. Objects move from positions of higher P.E to positions Lower P.E repulsive force attractive force U U r r 0 - Change of PE graph

12. repulsive force attractive force V r 0 Change of electric Potential V r 0 Electrical Potential always Decreases in direction of Electric Field Change of Electric Potential Graph

13. áNegative charge moves in opposite direction to electric field áPositive charge moves in the same direction as an electric field Movement of Charge

14. áEquipotential Surface is áA connected set of points that all have the same electric potential áPotential Difference between points is 0 volts. Equipotential Surface

15. áNo work is done when moving charge from one to point to another point on such a surface áAs change of P.E. between points on surface is 0 Joules Work done on Surface

16. Implications

17. +3C -2C Field lines and Equipotential Surfaces

18. Review of Gauss' Law I Gauss’ Law The Electric Flux through a surface enclosing a charge is equal to the Charge enclosed divided by the permittivity The Electric Field outside of a spherical charged object is the same as if object were a point charge

19. Review of Gauss' Law II Gauss’ Law

20. Review of Gauss' Law III

21. áSurface of an isolated conductor in electrostatic equilibrium must be an isopotential surface Implications

22. Electric Potential of Point Charge

23. Electric Potential of Point Charge II Field and Potential from point charge

24. Picture unit vector point where electric field and potential is evaluated r Charge

25. Polar Coordinates

26. Phi Theta x y z (x,y,z) r Definitions of coordinates

27. Position vector in Polar Coordinates

28. Electric Field and Potential for Point Charge

29. distance from center of charged conductor radius of conductor = Electric Potential = Electric Field Magnitude Graphs

30. Electric Field and Electric Potential outside of spherical charged conductor is the same as the field and potential obtained from a point charge that has the same charge Spherical Charge

31. Electric Potential due to many Sources Electric Potential at a point due to many source charges V( r 0 )  V i ( r 0 )  i  k Q i r 0 i i  V( r 0 )  V(r) charged body  dr= k  ( r ) r charged body  d r

32. Potential Energy of Interaction I Potential Energy of Interaction Potential energy of interaction between source charge of electric field and the charge Q Q Fixed source charge Q 0 and fixed charge Q

33. Potential Energy of Interaction II áP.E. of interaction between Q and Q 0 (source charge) - positive work is done on the charges in bringing them together if they repel or negative work if they attract áIf one brings another charge to a fixed position work will be done (either positive or negative) by the forces due to Q and Q 0

34. Potential Energy of Interaction III