Electrical Potential Energy & Electrical Potential

1. Electrical Potential Energy& Electrical Potential

2. Gravitational Potential Energy Energy an object with mass has by virtue of its position in a gravitational field

3. Galileo Galilea

4. Mass in Uniform Gravitational Field y x m yi mg Define Ugrav such that, yf Earth’s Gravitational Field

5. Gravitational Potential Difference Mass in uniform field Difference in Gravitational Potential Energy Mass of Object Moving Under Field’s Influence Define the Gravitational Potential Difference between two points in the field as: Property of field!

6. Electrical Potential Energy Energy an object with charge has by virtue of its position in an electrical field

7. Charge in Uniform Electrical Field y +q yi x qE Define Uelec such that, yf Between Capacitor Plates

8. Electrical Potential Difference Charge in uniform field Difference in Electrical Potential Energy Charge of Object Moving Under Field’s Influence Define the Electrical Potential Difference between two points in the field as: Property of field!

9. Electrical Potential Difference To calculate the electrical potential difference between two points in an electric field: Calculate the work done by the field in moving a positive test charge from the one point to the otherdivided by the charge of the test charge

10. Electrical Potential Difference

11. Electrical Potential Energy at a Point In most cases it is the difference in potential energy between two points that is important. However, if the potential energy of a charge at a point is required, then a reference point has to be chosen and the potential energyof the charge defined to be zero at that point. In electrostatics, this reference point is usually taken to be at infinity.

12. Electrical Potential at a Point To arrive at a property of the field, dependent only on the source charges setting up the field, we define the electrical potential at a pointP in the field as … … the electrical potential energy of a small test chargeplaced at the point P divided by the charge on the test charge, Unit: J.C-1 or V

13. Electrical Potential at a Point In terms of work done:

14. Electrical Potential Charge with Potential Energy +Q +q

15. Electrical Potential Source generates a potential at this position +Q Potential exists even in the absence of a charge to experience it

16. Electrical Potential Charge with Potential Energy +Q +q

17. Electrical Potential Due to a Point Charge Include sign of Q • Potential due to positive source charge is positive • Potential due to negative source charge is negative

18. Electrical Potential Differencein the Electric Field of a Point Charge (Potential Difference between pointsAandB)

19. Example 1 Y&G Q4 Page 611 A point charge q1 = +2.40mC is held stationary at the origin. A second point charge q2 = -4.30mC moves from point A with x= 0.150 m, y = 0, to point B with x = 0.250 m, y = 0.250 m. • How much work is done by the electric field on q2? • What is the difference in the electrical potential energy of q2? • What is the potential difference between the points A and B?

20. Electrical Potential Due to Multiple Point Charges The electrical potential at position P due to a system of N source point charges is given by: Include sign of Qi Principle of Superposition

21. Example 2 Y&G Q22 Page 612 Two point charges q1 = +2.40 nC and q2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q1 and 0.060 m from q2. Find, • the potential at point A; • the potential at point B; • the work done by the electric field on a charge of 2.50 nC that travels from B to A.

22. Example 3 HRW7 637 SP24-4 Twelve electrons are equally spaced around a circle of radius R. R C a)What is the electric potential at the centre C ? (Assume V = 0 at infinity) b) What is the electric field at C ?

23. Example 4 HRW7 637 SP24-4 The electrons are now moved around the circle until they are spread over a non-uniformly spaced 120 arc. R 120° C • What is the electric potential at the centre C? (Assume V = 0 at infinity.) • What is the electric field at C?

24. Example 5 A -10.0 nC point charge and a +20.0 nC point charge are 15 cm apart on the x-axis. a) What is the electric potential at the point on the x-axis where the electric field is zero? b) What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

25. 2 conductors near one another but not touching Capacitors Parallel-Plate Capacitor: d USE: capacitors store electric charge Charge by connecting to battery Separation of charge causes potential difference between the plates:

26. Potential Difference in a Capacitor

27. Example 6 In the figure beside, a proton is fired with a speed of 200 000 m/s from the midpoint of the capacitor toward the positive plate. Show that this is insufficient speed to reach the positive plate. What is the proton’s speed as it collides with the negative plate?

28. Capacitors Capacitance Usually replace DVjust by V [ C ] = C.V-1 = farad (F)

29. Something to Think About Why does a bird sitting on a high voltage power line not get shocked?