1. Warm-Up: April 6/7, 2016  A black sphere with charge of 3.3 µC is pulled towards a gold sphere 4.7 cm away. The attractive force is 6.2 N. What is the charge of the gold sphere? -4.6x10 -7 C

2. Homework Questions?

3. Chapter 21

4. Field Theory of Gravity  Objects with mass curve spacetime  Gravity is a result of this change in spacetime  The force of gravity on an object is due to the local shape of spacetime  We call this result a “gravitational field”  Near Earth, the gravitational field strength is 9.8 N/kg (=9.8 m/s 2 )

5. Electric Fields  Just like mass creates a gravitational field, charge creates an electric field  Electric field is a vector field (has direction and magnitude)  The electric field points towards negative charges, and away from positive charges

6. - +

7. Electric Field Strength  Represented by a capital “E”  Has units of Newtons per Coulomb, N/C  Is equal to the force on a charged object (called the test charge) divided by the amount of charge in the object

8. Example 1  A negative test charge of 4.32 µC is in an electric field that exerts 1.81 mN on it. What is the magnitude of the electric field at the location of the test charge? 419 N/C

9. You-Try #1  A positive test charge of 7.56 µC is in an electric field that exerts 9.38x10 -4 N on it. What is the magnitude of the electric field at the location of the test charge? 124 N/C

10. Direction of E and F E  If the test charge is positive, E and F E are in the same direction  If the test charge is negative, E and F E are in opposite directions.

11. Example 2  A negative charge of 7.76 µC at rest in an electric field experiences a force of 1.18 N to the north. What is the magnitude and direction of the electric field? 1.52x10 5 N/C South

12. You-Try #2  A positive charge of 0.31 µC at rest in an electric field experiences a force of 0.45 N to the west. What is the magnitude and direction of the electric field? 1.5x10 6 N/C west

13. Electric Field Lines  Electric field lines are curves in pictures of electric fields that show the direction and relative magnitude of the field  The closer the lines, the stronger the field

14. Two Positive Charges

15. One Positive, One Negative

16. Warm-Up:  A positive charge of 4.13 µC at rest in an electric field experiences a force of 4.9 N up. What is the magnitude and direction of the electric field?

17. Comparing Mass and Charge Mass  Gravity Charge  Electric

18. Example 3  What is the magnitude and direction of the electric field 1.3 meters east of a point charge of +4.7 µC? 25000 N/C east

19. You-Try #3  What is the magnitude and direction of the electric field 0.93 meters south of a point charge of -5.1 µC? 53000 N/C north

20. Electric Potential Difference

21.  The ratio of the work needed to move a charge to the strength of the charge.  Also equal to the product of electric field strength and distance the charge moves

22. Electric Potential Difference  When the electric potential difference between two or more points is zero, they are at equipotential.  Electric potential difference is measured with a voltmeter.  Electric potential difference is sometimes called voltage outside the physics classroom. Don’t confuse it with the unit, Volts

23. Example 4  A voltmeter reads 470 V across two charged, parallel plates that are 0.030 m apart. What is the electric field strength between them? 16000 N/C 1.6x10 4 N/C

24. You-Try #4  The electric field intensity between two large, charged, parallel plates is 5250 N/C. The plates are 0.0475 m apart. What is the electric potential difference between them? 249 V

25. Formula Recap

26. Example 5  What work is done when 1.4x10 -2 C is moved through an electric potential difference of 2.5 V? 0.035 J 3.5x10 -2 J

27. You-Try #5  What work is done when 7.1x10 -3 C is moved through an electric potential difference of 1.8 V? 0.013 J 1.3x10 -2 J

29. Warm-Up:  What is the magnitude and direction of the electric field 1.21 meters south of a point charge of +8.25 µC? 51000 N/C south 5.1x10 4 N/C south

30. Millikan Oil-Drop Experiment  In 1909, Robert Andrews Millikan conducted his famous oil-drop experiment  The experiment provided the charge of the electron, 1.60x10 -19 C

32. You-Try #6 A. Draw a free body diagram for an oil drop that is suspended (not moving) in Millikan’s oil-drop apparatus. B. Write a formula for the forces acting on the oil drop. C. What did Millikan need to know in order to determine the charge of an electron?

33. Capacitors  A capacitor is a device used to store charge  Capacitors are widely used in electronic devices  A capacitor has a constant capacitance, C.  Capacitance is measured in Farads, F.

34. Capacitor Examples  Capacitors typically have a capacitance between 1.0x10 -11 F and 5.0x10 -4 F.

35. Example 7  An 81 nF capacitor has an electric potential difference of 25 V across it. What is the charge on the capacitor? 2.0x10 -6 C

36. You-Try #7  A 51 nF capacitor has an electric potential difference of 7.9 V across it. What is the charge on the capacitor? 4.0x10 -7 C

37. Assignments  Read Chapter 21  Page 584 #42-46, 58-61, 66-69, 76-79, 84-86  Chapter 20 Review Worksheet  Chapter 21 Review Worksheet  Optional advanced reading: OpenStax Chapter 18