1. Electric Potential, Electric Potential Energy, and the Generalized Work Energy Theorem

2. When an object is lifted at a constant velocity the work done equals the change in the object’s gravitational potential energy. Because the gravitational force is conservative the work done only depends on the initial and final heights and not on the path followed between the two points. Gravitational Potential Energy and the Gravitational Potential

3. Moving an Object in a Gravitational Field 1 3 2

4. Electric Potential Energy and the Electric Potential Since the electric force (field) is conservative we can define an Electric Potential Energy, EPE and an Electric Potential,  E. The electric potential energy of a charge q located at some point in an electric field E produced by some charge distribution is defined as:

5. Total Mechanical Energy and the Generalized Work-Energy Theorem The total mechanical energy of a charged object is: The Generalized Work-Energy Theorem becomes:

6. Electric Potential due to Various Charge Distributions A) Single point charge, q 1

7. B) Multiple point charges, q i

8. C) Electric potential inside a parallel-plate capacitor carrying equal and opposite charges +/- q 1

9. Examples

10. Three point charges, q 1 = 25  C, q 2 = -40  C, and q 3 = 60  C lie on a straight line as shown below. What is the electric potential,  E at point P, 5.5m from the origin?

12. How much work would be required to bring a proton from infinity and place it at point P? (Ignore any changes in the proton’s KE or GPE) Work must be done ON the proton to bring it from infinity and place it at point P

13. Two point charges, q 1 = 25  C and q 2 = -40  C lie on a straight line as shown below. For the electric potential to be zero the potentials due to q 1 and q 2 must cancel. To cancel the potentials must be equal in magnitude and opposite in sign. There are three possibilities for the location of a point where the electric potential is zero. 1. To the right of q 2, x > 4m. 2. Between q 1 and q 2, 0 < x < 4m. 3. To the left of q 1, x < 0. Is there a point where the electric potential is zero?

14. Between q 1 and q 2, 0 < x < 4m. Since q 1 <q 2 the point must be closer to q 1.

16. To the left of q 1, x < 0. Any point to the left of q 1 must be closer to q 1.

19. An object with a mass of 0.05kg and charge of 2.0x10 -7 C is ejected from the negative plate of a capacitor with an initial velocity of 15m/s as shown below. The plates of the capacitor are 5m apart and each has an area of.01m 2. The plates carry equal and opposite charges of 4x10 -7 C. Will the object reach the positive plate?

20. As the object moves the only forces acting on it are the gravitational and electrical forces both of which are conservative. Therefore the total mechanical energy of the object will be conserved. The negative plate is chosen as the reference level for both the gravitational and electric potential energy. Therefore:

21. Let’s find the height, h f, where the object stops moving upward, v f = 0.

22. The object does not reach the upper plate. What minimum initial velocity would allow the object to reach the upper plate?