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Lecture 4: May 27 th 2009

This lecture covers the concept of electric potential and potential energy in physics, including the work done on a charge by electric force along a closed path and the change in electric potential energy. It also explains the relationship between work and energy, units of electric potential, and the calculation of electric field from electric potential.

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Lecture 4: May 27 th 2009

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  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

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