and Discrete Charge Distributions

Size: px

Start display at page:

Download "and Discrete Charge Distributions"

Ruth Lang
5 years ago
Views:

1 Module 03: Electric Fields and Discrete Charge Distributions 1

2 Module 03: Outline Review: Electric Fields Charge Dipoles 2

3 Last Time: Gravitational & Electric Fields 3

4 Gravitational & Electric Fields SOURCE: Mass M Charge q s s (±) CREATE: r g = G r M s rˆ 2 r E q = k e r s r ˆ 2 FEEL: r F g r r = mg r F = q E E This is easiest way to envision field, as producing forces! 4

5 Electric Field Lines 1. Direction of field at any point is tangent to field line at that t point 2. Field lines point away from positive charges and terminate on negative charges 3. Field lines never cross each other 5

6 Concept Questions on Electric Field 6

7 Concept Question: Force The picture shows the field lines around two charges. The force between the two charges is: 1. Attractive 2. Repulsive 3. Can t tell without more information 4. I don t know 7

8 Concept Question: Field Lines Electric field lines show: 1. Directions of forces that exist in space at all times. 2. Directions in which positive charges on those lines will accelerate. 3. Paths that charges will follow. 4. More than one of the above. 5. I don t know. 8

Point P lies along the perpendicular bisector of the line joining

9 Checkpoint Problem P s ĵ î q d + q Consider two point charges of equal magnitude but opposite signs, separated by a distance d. Point P lies along the perpendicular bisector of the line joining the charges, a distance s above that line. What is the E field at P? 9

10 Two Concept Questions: E Field of Finite # of Point Charges 10

11 Concept Question: Equal Charges 1. 1 Electric field at P is: r 2 kqs r e ˆ 2kqd e 1. E = j 2. E = ˆ i 2 3/2 2 3/2 2 d 2 d s + s r 2 kqd r e ˆ 2kqs e 3. E = j 4. E = ˆi 2 3/2 2 3/2 2 d 2 d s + s I Don't Know 11

The electric field at the center of the hexagon (at point

12 Concept Question: 5 Equal Charges Six equal positive charges q sit at the vertices of a regular hexagon with sides of length R. We remove the bottom charge. The electric field at the center of the hexagon (at point P) is: r E kq r ˆ kq = j 2. E = ˆj 2 2 R R r kq r 3. ˆ kq E = j 4. E = ˆj 2 2 R R r 5. E = 0 6. I Don't Know 12

13 Charging 13

14 How Do You Get Charged? Friction Transfer (touching) Induction q Neutral

15 Demonstrations: Instruments for Charging 15

16 Electric Dipoles A Special Charge Distribution 16

17 Electric Dipole Two equal but opposite charges +q and q, separated by a distance 2a r p q -q 2a Dipole Moment: Vector product of charge with displacement r p = q 2 a ˆ j = 2 qaˆ j r p points from negative to positive charge 17

18 Why Dipoles? Nature Likes To Make Dipoles! Animation 18

19 Dipoles make Fields 19

20 Electric Field Created by Dipole Thou shalt use components! t! r r ˆr r Δ x Δ y = = i + ˆ r r r r ˆj E x = k e q Δx Δx x 3 3 = k e q x r ) 3/2 ) 3/2 + r x 2 +(y a) 2 x 2 +(y +a) 2 Δy y Δy a + a E y = k e q + y 3 3 r + r = k q y y e x 2 + (y a) 2 3/2 x 2 + (y + a) 2 3/2 20

21 Concept Question Question: Dipole Fall-Off 21

22 Concept Question: Dipole Field As you move to large distances r away from a dipole, the electric field will fall-off as: 1. 1/r 2, just like a point charge 2. More rapidly than 1/r 2 3. More slowly than 1/r 2 4. I Don t Know 22

23 Concept Question Answer: Dipole Field Answer: 2) More rapidly than 1/r 2 We know this must be a case by thinking about what a dipole looks like from a large distance. To first order, it isn t there (net charge is 0), so the E-Field must decrease faster than if there were a point charge there. 23

24 Point Dipole Approximation Take the limit r >> a Finite it Dipole You can show E x 3p p 4πε 0 r sinθ cosθ 3 Point Dipole ( ) E p 3cos 2 θ 1 y 4πε r

25 Shockwave for Dipole Dipole Visualization 25

26 Dipoles feel Fields 26

27 Demonstration: Dipole in Field 27

28 Dipole in Uniform Field r E = Eˆ i r p= 2 qa (cos θˆ i + sin θˆ j ) r r r r r Total Net Force: F = F + F = qe+ ( q) E= 0 net + r r r Torque on Dipole: = r F r r τ = p E ( )( ) τ = rf sin(θ) = 2a qe sin( θ ) = pe sin( θ ) + p r tends to align with the electric field 28

29 Torque on Dipole Total Field (dipole + background) shows torque: Animation (link) Field lines transmit tension Connection between dipole field and constant field pulls dipole into alignment 29

30 Concept Question Question: Dipole in Non-Uniform Field 30

31 Concept Question: Dipole in Non- E Uniform Field A dipole sits in a non-uniform electric field E, as shown 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 31

32 MIT OpenCourseWare SC Physics II: Electricity and Magnetism Fall 2010 For information about citing these materials or our Terms of Use, visit:

Electric Fields, Dipoles and Torque Challenge Problem Solutions

Electric Fields, Dipoles and Torque Challenge Problem Solutions Problem 1: Three charges equal to Q, +Q and +Q are located a distance a apart along the x axis (see sketch). The point P is located on the