1. 1 W02D1 Electric Dipoles and Continuous Charge Distributions

2. Announcements Math Review Tuesday Tues Feb 14 from 9-11 pm in 32-082 PS 1 due Tuesday Tues Feb 14 at 9 pm in boxes outside 32-082 or 26-152 W02D2 Reading Assignment Course Notes: Chapter Course Notes: Sections 4.1-4.2, 4.7 Make sure your clicker is registered 2

3. 3 Outline Electric Dipoles Force and Torque on Dipole Continuous Charge Distributions

4. 4 Nature Likes to Make Dipoles http://youtu.be/EMj10YIjkaY

5. 5 Demonstration: Dipole in a Van de Graaff Generator D22

6. 6 Concept Question: Dipole in Non- Uniform Field A dipole sits in a non-uniform electric field E E Due to the electric field this dipole will feel: 1.force but no torque 2.no force but a torque 3.both a force and a torque 4.neither a force nor a torque

7. 7 Concept Question Answer: Non- Uniform Field Because the field is non-uniform, the forces on the two equal but opposite point charges do not cancel. As always, the dipole wants to rotate to align with the field – there is a torque on the dipole as well Answer: 3. both force and torque E

8. 8 Continuous Charge Distributions

9. 9 V Break distribution into parts: E field at P due to  q Superposition:

10. 10 Continuous Sources: Charge Density

11. 11 Group Problem: Charge Densities A solid cylinder, of length L and radius R, is uniformly charged with total charge Q. (a)What is the volume charge density ρ? (b)What is the linear charge density λ? (c)What is the relationship between these two densities ρ and λ?

12. 12 Examples of Continuous Sources: Finite Line of Charge E field on perpendicular bisector

13. 13 Examples of Continuous Sources: Finite Line of Charge E field off axis

14. 14 Examples of Continuous Sources: Finite Line of Charge Grass seeds of total E field

15. 15 Concept Question Electric Field of a Rod A rod of length L lies along the x-axis with its left end at the origin. The rod has a uniform charge density λ. Which of the following expressions best describes the electric field at the point P

16. 16 Concept Question Electric Field of a Rod: Answer A rod of length L lies along the x-axis with its left end at the origin. The rod has a uniform charge density λ. Which of the following expressions best describes the electric field at the point P

17. 17 Group Problem: Line of Charge Point P lies on perpendicular bisector of uniformly charged line of length L, a distance s away. The charge on the line is Q. Find an integral expression for the direction and magnitude of the electric field at P.

18. 18 Hint on Line of Charge Group Problem Typically give the integration variable (x’) a “primed” variable name. ALSO: Difficult integral (trig. sub.)

19. 19 E Field from Line of Charge Limits: s >> L (far away) and s << L (close) Looks like the E field of a point charge if we are far away Looks like E field of an infinite charged line if we are close

20. 20 Examples of Continuous Sources: Ring of Charge E field on the axis of the ring of charge

21. 21 Examples of Continuous Sources: Ring of Charge E field off axis and grass seeds plot

22. A uniformly charged ring of radius a has total charge Q. Which of the following expressions best describes the electric field at the point P located at the center of the ring? 22 Concept Question Electric Field of a Ring

23. 23 Concept Question Electric Field of a Ring: Answer A uniformly charged ring of radius a has total charge Q. Which of the following expressions best describes the electric field at the point P located at the center of the ring?

24. 24 Demonstration Problem: Ring of Charge A ring of radius a is uniformly charged with total charge Q. Find the direction and magnitude of the electric field at the point P lying a distance x from the center of the ring along the axis of symmetry of the ring.

25. 25 Ring of Charge Symmetry! 1) Think about it 2) Define Variables

26. 26 Ring of Charge 3) Write Equation

27. 27 Ring of Charge 4) Integrate This particular problem is a very special case because everything except dq is constant, and

28. 28 Ring of Charge 5) Clean Up 6) Check Limit

29. 29 Group Problem: Uniformly Charged Disk P on axis of disk of charge, x from center Radius R, charge density . Find E at P

30. 30 Disk: Two Important Limits Limits: x >> R (far) and x << R (close) Looks like E of a point charge far away Looks like E field of an infinite charged plane close up

31. 31 Scaling: E for Plane is Constant 1) Dipole: E falls off like 1/r 3 2) Point charge:E falls off like 1/r 2 3) Line of charge:E falls off like 1/r 4) Plane of charge: E constant