Lecture 4: May 27 th 2009

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

2. 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. • In other words: Electrostatic force is a conservativeforce.  An electric potential (a scalar quantity) can be defined. (just like we did with the gravitational force / potential) + a Physics for Scientists and Engineers II , Summer Semester 2009

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

4. Change in Electric Potential Energy • Imagine a charge q0 is moved in an electric field along some path + Physics for Scientists and Engineers II , Summer Semester 2009

5. 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 !!! Physics for Scientists and Engineers II , Summer Semester 2009

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

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

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

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

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

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

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

13. Electric Potential and Potential Energy due to Point Charges B A q Again, DU is independent of the path chosen, confirming that the electric force is conservative. Potential energy change when moving a charge q0 in the electric field of charge q from A to B. Physics for Scientists and Engineers II , Summer Semester 2009

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

15. Electric Potential due to Multiple Point Charges Potential Energy of a System of Two Point Charges Assume charge q2 is already in place. Then, a charge q1 is brought from a very large distance (“infinity”) near charge q2 using an external force. Electric potential due to the electric field of charge q2. • Bringing two like charges together requires positive work by an external force. • When two unlike charges are brought together, negative work is done by an external force. Physics for Scientists and Engineers II , Summer Semester 2009

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

17. q1 q1 q2 q2 Electric Potential Energy of Collection of Point Charges 1) Initially, we have only one charge (q1): 2) Next, a second charge (q2) is brought near the charge already in place (q1) : Physics for Scientists and Engineers II , Summer Semester 2009

18. q1 q2 q3 q3 Adding the Third Charge …. 3) Finally, a third charge (q3) is brought near the charges already in place (q1and q2) : Physics for Scientists and Engineers II , Summer Semester 2009

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