1 W02D1 Electric Dipoles and Continuous Charge Distributions

Announcements Math Review Tuesday Week Two Tues from 9-11 pm in PS 1 due Week Two Tuesday Tues at 9 pm in boxes outside or W02D2 Reading Assignment Course Notes: Chapter Course Notes: Sections , 3.6, 3.7, 3.10 Make sure your clicker is registered 2

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

4 Nature Likes to Make Dipoles

5 Demonstration: Electric field Lines D16

6 Dipole in Uniform Field Total Net Force: Torque on Dipole: tends to align with the electric field

7 Torque on Dipole Total Field (dipole + background) shows torque: Field lines transmit tension Connection between dipole field and constant field “pulls” dipole into alignment

8 Demonstration: Dipole in a Van de Graaff Generator D22

9 Demonstration: Bouncing Balloon Van de Graaf Generator D17

10 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

11 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

12 Continuous Charge Distributions

13 V Continuous Charge Distributions Break distribution into parts: E field at P due to Superposition:

14 Continuous Sources: Charge Density

15 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?

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

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

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

19 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

20 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

21 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.

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

23 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

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

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

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? 26 Concept Question Electric Field of a Ring

27 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?

28 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.

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

30 Ring of Charge 3) Write Equation

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

32 Ring of Charge 5) Clean Up 6) Check Limit

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

34 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

35 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