1. Physics 212 Lecture 1, Slide 1 Physics 212 Lecture 1 Today's Concepts: a) Coulomb’s Law b) Superposition 02 Original: Mats Selen Modified: W.Geist

2. My web page: http://facstaff.gpc.edu/~wgeist/http://facstaff.gpc.edu/~wgeist/ Homework: www.masteringphysics.com 20%www.masteringphysics.com Pre-class assignments are due before class! 3exams + 1 final: 75% I<clickers: 5% Book: P.A Tipler, G. Mosca "Physics for Scientists and engineers", 6'th edition. Mc Dermott et al: Tutorials in Introductory physics Check the web page and print them out before class! Get your i-clickers from the bookstore.

3. Warm up exercise Which force is larger? A) the force of the apple on the earth. B) The force of the earth on the apple. C)The same Newton’s law of gravity: Force by earth on apple = Force by apple on earth Physics 212 Lecture 1, Slide 3

4. Physics 212 Lecture 1, Slide 4 Coulomb’s Law: q1q1q1q1 q2q2q2q2 The force on a charge due to another charge proportional to the product of the charges and inversely proportional to the separation squared. r q1q1q1q1 q2q2q2q2 The force is always parallel to a line connecting the charges, but the direction depends on the signs of the charges: q1q1q1q1 q2q2q2q2 Opposite signs attract q1q1q1q1 q2q2q2q2 Likes signs repel 07

5. Physics 212 Lecture 1, Slide 5 Pith balls Take two pith balls and charge them both with a plastic rod. After you charged them they will: A) Attract each-other B) Repel each-other C) Either – it depends on the material of the cloth 10

6. Physics 212 Lecture 1, Slide 6 If the same thing is done to both balloons they will acquire the same sign charge. They will repel ! + + + + + + + + Pith balls 11

7. Conductors and Insulators Conductor is an object where charge moves along or through. Insulator is an object where the charge does not move. Notice: You can charge the glass and plastic, hence an insulator can be charged, but the charge is stuck on the surface and cannot move.

8. Conductors and Insulators Where is the charge on the conductor? Charge is transferred to the box by contact. Charge moves freely through metal. Like charges repel each other. Consequently, charge placed on a metal will quickly spread as far as possible and will charge the entire metal surface. This is in contrast to the charge placed on an insulator. The time for the charge to spread out on a conductor is "instantaneous" as far as simple experiments are concerned.

9. Polarization of a metal Aluminumfoil

10. Why is the aluminum foil lifted off the ground? Aluminumfoil

11. Coulomb’s Law:F~1/r 2 Aluminumfoil F +on- -F +on+ > mg F +on- F +on+

12. Induction AB -- - - - AB - - --+ + + + -- - - - A B - - --+ ++ + B - - - - A + + + + Two metal spheres mounted on insulating stands. 1.Make the spheres touch 2.Bring a charged rod near one of the spheres 3.Separate the spheres 4.Remove the charged rod

13. Clicker Question: Induction A positively charged object is placed close to a conducting object attached to an insulating glass pedestal (a). After the opposite side of the conductor is grounded for a short time interval (b), the conductor becomes negatively charged (c). Based on this information, we can conclude that within the conductor: 1. both positive and negative charges move freely. 2. only negative charges move freely. 3. only positive charges move freely. 4. We can’t really conclude anything. - - - ++++++++

14. Physics 212 Lecture 1, Slide 14 Coulomb’s Law q1q1q1q1 q2q2q2q2 14 Our notation is the force by 1 on 2 (think “by-on ”) is the force by 1 on 2 (think “by-on ”) is the vector that points from 1 to 2. is the vector that points from 1 to 2.Examples If the charges have the same sign, the force by charge 1 on charge 2 would be in the direction of r 12 (to the right) If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direction of r 12 (left) q1q1q1q1 q2q2q2q2

15. Physics 212 Lecture 1, Slide 15 Example: Coulomb Force Two paperclips are separated by 10 meters. Then you remove 1 electron from each atom on the first paperclip and place it on the second one. k= 9 x 10 9 N m 2 / C 2 electron charge = 1.6 x 10 -19 Coulombs N A = 6.02 x 10 23 What will the direction of the force be? A) Attractive B) Repulsive 16

16. Physics 212 Lecture 1, Slide 16 Example: Coulomb Force Two paperclips are separated by 10 meters. Then you remove 1 electron from each atom on the first paperclip and place it on the second one. m A =27 k= 9 x 10 9 N m 2 / C 2 electron charge = 1.6 x 10 -19 Coulombs N A = 6.02 x 10 23 Which weight is closest to the approximate force between those paperclips (recall that weight = mg, g = 9.8 m/s 2 )? A) Paperclip (1g x g) B) Text book (1kg x g ) C) Truck (10 4 kg x g ) D) Aircraft carrier (10 8 kg x g) E) Mt. Everest (10 14 kg x g ) 20

17. Physics 212 Lecture 1, Slide 17 Example: Coulomb Force Two paperclips are separated by 10 meters. Then you remove 1 electron from each atom on the first paperclip and place it on the second one. k= 9 x 10 9 N m 2 / C 2 electron charge = 1.6 x 10 -19 Coulombs N A = 6.02 x 10 23 Number of electrons on a 1g aluminum: N = N A /27 F = k N e N e /100m 2 = 9 x 1.6 x 1.6 x 6/27 x 6/27 x 10 9+23+23-19-19-2 = 10 15 N F(MtEverest) = 9.8x 10 14 N 20

18. Physics 212 Lecture 1, Slide 18 The forces are equal and opposite. This is due to Newton's third law. 22

19. Physics 212 Lecture 1, Slide 19 Charges on Strings Two balls of equal mass are suspended from the ceiling with non-conducting wire. One ball is given a charge +3q and the other is given a charge +q. g +q+q+3q Which of the following best represents the equilibrium positions? (b)(a) +3q +q+q (c) +3q +q+q +q+q 25

20. Physics 212 Lecture 1, Slide 20 Charges on Strings Which best represents the equilibrium position? Remember Newton’s Third Law! F 31 = -F 13 +3q +q+q +q+q +q+q (b)(a) (c) 26

21. Physics 212 Lecture 1, Slide 21 The forces between Q1 and Q3 are equal and opposite, satisfying Newton's third law. 27

22. Physics 212 Lecture 1, Slide 22 Superposition: q1q1q1q1 q2q2q2q2 If there are more than two charges present, the total force on any given charge is just the vector sum of the forces due to each of the other charges: q3q3q3q3 q4q4q4q4 F 2,1 F 3,1 F 4,1 F1F1F1F1 F 2,1 F 3,1 F 4,1 F1F1F1F130

23. Physics 212 Lecture 1, Slide 23 What happens to Force on q 1 if its sign is changed q1q1q1q1 q2q2q2q2 q3q3q3q3 q4q4q4q4 A)|F 1 | increases B)|F 1 | remains the same C)|F 1 | decreases D)Need more information to determine Superposition ACT 32

24. Physics 212 Lecture 1, Slide 24 q1q1q1q1 q2q2q2q2 The direction of all forces changes by 180 o – the magnitudes stay the same: q3q3q3q3 q4q4q4q4 F 2,1 F 3,1 F 4,1 F1F1F1F1 F 2,1 F 3,1 F 4,1 F1F1F1F1 33 q1q1q1q1 q2q2q2q2 q3q3q3q3 q4q4q4q4 F 2,1 F 3,1 F 4,1 F1F1F1F1 F 2,1 F 3,1 F 4,1 F1F1F1F1

25. Physics 212 Lecture 1, Slide 25 Coulomb Force simulation

26. Physics 212 Lecture 1, Slide 26 Since there are both a positive and negative charge in Case 2, some of the force will be cancelled out when the vectors are summed. In Case 1 and 3 the magnitude will be the same whether the charge is positive or negative. simulation Preflight 3 35

27. Physics 212 Lecture 1, Slide 27 If Q4 was positive, the two + charges would result in a vector pointing in the direction exactly opposite and equal in magnitude to the vector pointing toward the negative charge. The same is true is Q4 was negative. A B C 38

28. Physics 212 Lecture 1, Slide 28 Example Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring q q q 3q What is horizontal force on Q? A) F x > 0 B) F x = 0 C) F x 0 B) F x = 0 C) F x < 0 x y Q 41

29. Physics 212 Lecture 1, Slide 29 Example Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring q q q 3q What is vertical force on Q, if Q has same sign charge as q? A) F y > 0 B) F y = 0 C) F y 0 B) F y = 0 C) F y < 0 x y Q 41

30. Physics 212 Lecture 1, Slide 30 Solution Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring q q q 3q Q Case 1: Q same sign charge as q x y 47 =

31. Physics 212 Lecture 1, Slide 31 Example Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring q q q 3q What is vertical force on Q, if Q has opposite sign charge as q? A) F y > 0 B) F y = 0 C) F y 0 B) F y = 0 C) F y < 0 x y Q 41

32. Physics 212 Lecture 1, Slide 32 Solution Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring q q q 3q Q Case 2: Q opposite sign charge as q x y 47 =

33. Physics 212 Lecture 1, Slide 33 Try using our Coulomb Force simulation

34. ++++++++ ++++++++ ++++++++ +Q +Q +Q + +q θθ s s s For the following charge distribution, find the net Coulomb force on the +q charge. (Q=10nC, q=1nC, s=10cm, θ=30 0 ) A)F= 2.5 x 10 -6 N B)F= 5.5 x 10 -6 N C)F= 0N D)F= 0.5 x 10 -6 N Solution: See lect 02