1. Physics for Scientists and Engineers II, Summer Semester 2009 Lecture 4: May 27 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 In other words: Electrostatic force is a conservative force.  An electric potential (a scalar quantity) can be defined. (just like we did with the gravitational force / potential) Work Done on Charge by Electric Force Along a Closed Path + Imagine a charge in an electric field is moved by external force as shown in a closed path. a

3. Physics for Scientists and Engineers II, Summer Semester 2009 Remember from Physics 2215

4. Physics for Scientists and Engineers II, Summer Semester 2009 Change in Electric Potential Energy + Imagine a charge q 0 is moved in an electric field along some path

5. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential Energy An absolute potential energy can be defined relative to some position, where arbitrarily the potential energy is set to be U = 0 (like in gravitational PE) Electric Potential The electric potential energy depends not only on the location of the charge and the location of U = 0, but also on the amount of charge itself. A quantity independent of charge can be defined: The electric potential V. Never confuse potential and potential energy !!!

6. Physics for Scientists and Engineers II, Summer Semester 2009 Work – Energy Relationship Units of Electric Potential

7. Physics for Scientists and Engineers II, Summer Semester 2009 Other Useful Units

8. Physics for Scientists and Engineers II, Summer Semester 2009 Potential Difference in a Uniform Field AB

9. Physics for Scientists and Engineers II, Summer Semester 2009 Potential Energy Difference in a Uniform Field AB

10. Physics for Scientists and Engineers II, Summer Semester 2009 Non-parallel displacement A B 

11. Physics for Scientists and Engineers II, Summer Semester 2009 - + Electron “Gun” -------- ++++++++ - A B - d

12. Physics for Scientists and Engineers II, Summer Semester 2009 Electron “Gun” -------- ++++++++ -- 5.0cm

13. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential and Potential Energy due to Point Charges q A B Again,  U is independent of the path chosen, confirming that the electric force is conservative. Potential energy change when moving a charge q 0 in the electric field of charge q from A to B.

14. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential due to Point Charges; Choosing Zero Point q A B

15. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential due to Multiple Point Charges Potential Energy of a System of Two Point Charges Assume charge q 2 is already in place. Then, a charge q 1 is brought from a very large distance (“infinity”) near charge q 2 using an external force. Electric potential due to the electric field of charge q 2. 1)Bringing two like charges together requires positive work by an external force. 2)When two unlike charges are brought together, negative work is done by an external force.

16. Physics for Scientists and Engineers II, Summer Semester 2009 ++ --- + Potential energy increases (work done by external force is positive) Potential energy decreases (work done by external force is negative)

17. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Potential Energy of Collection of Point Charges q1q1 1) Initially, we have only one charge (q 1 ): 2) Next, a second charge (q 2 ) is brought near the charge already in place (q 1 ) : q1q1 q2q2 q2q2

18. Physics for Scientists and Engineers II, Summer Semester 2009 Adding the Third Charge …. 3) Finally, a third charge (q 3 ) is brought near the charges already in place (q 1 and q 2 ) : q1q1 q2q2 q3q3 q3q3

19. Physics for Scientists and Engineers II, Summer Semester 2009 Electric Field Calculation from Electric Potential