1. Units of Chapter 15 Electric Charge Electrostatic Charging Electric Force Electric Field Conductors and Electric Fields Gauss’s Law for Electric Fields: A Qualitative Approach Homework: 9, 13, 17, 20, 29, 31, 36, 47, 57, 76

2. 2 Electric Charge Transferred (not destroyed) Symbol: q, Q [coulomb, C] Q = ±Ne (N = integer, e = 1.6E-19 C) Like repel, Unlike attract, with force ~ 1/distance 2 Atom (Wilson)Atom /

3. 3 Charge and Matter ordinary matter: protons, neutrons, electrons proton charge = +1e neutron charge = 0 electron charge = -1e Conductors – one or more electrons are free to move Insulators - no free electrons

4. 4 Charging Friction: rub two dissimilar materials. Ex. wool rubbed against plastic results in + wool, and – plastic Induction: charged object near a conductor, induces charge separation /

5. 5 Coulomb’s Law q2q2 r q1q1 k e = 9.0 x 10 9 N m 2 /C 2.

6. 6 Example + + +1 nanocoulomb charge at origin, another +1 nanocoulomb charge is at x = 1 meter. force = 9E9(1E-9)(1E-9)/1x1 = 9E-9 N force on charge at origin is in “negative” direction force on charge at 1 meter is in “positive” direction ////

7. 7 Example - + -1 nanocoulomb charge at origin, +1 nanocoulomb charge is at x = 1 meter. force = 9E9(1E-9)(1E-9)/1x1 = 9E-9 N force on -charge at origin is in “positive” direction force on +charge at 1 meter is in “negative” direction does formula tell us these directions?

8. 8 3 or more charges force on each charge is vector sum of forces due to all other charges method: add x-components of all forces add y-components of all forces change to polar form if desired ////

9. 9 Example Force: 1) 10nC is at (0, 0.5) meters 2) -5nC is at (0.5, 0) meters Calculate force on 1nC at (0, 0). Force = 180nN Right + 360nN Down

10. 10 Fields what is fundamental: wind or force on sail? field or force on charge? How to define? wind: force per unit area field: force per unit charge /

11. 11 Electric Field Symbol: E [N/C] E = F/q E and F are parallel vectors wind exists at places without sails field exists at places without charges wind is independent of sail used to measure it field is independent of charge used to measure it

12. Electric Field Demo In oil http://video.google.com/videoplay?docid=879375962512 6360449&ei=bTbBSLaCEYrg- wHE57XoCQ&q=electric+field+lines&vt=lf&hl=enhttp://video.google.com/videoplay?docid=879375962512 6360449&ei=bTbBSLaCEYrg- wHE57XoCQ&q=electric+field+lines&vt=lf&hl=en On a flame: http://www.youtube.com/watch?v=MPFkp2 HrEcshttp://www.youtube.com/watch?v=MPFkp2 HrEcs

13. 13 Field due to Point Charge What is field around charge Q? field is force on another charge, q, divided by the size of charge of q if q is “r” meters from Q, then Force F = kQq/r 2. field E = F/q = (kQq/r 2 )/q = kQ/r 2. field around Q does not depend on q. E is outward if Q is +, inward if Q is - //

14. 14 Electric Field Lines Drawn parallel to the electric field Arrows tell us the direction of E Density of lines tells us the strength of E + charges move in direction of arrows - charges move in opposite dir. of arrows

15. 15 Field Example Q = +4nC at origin, “P” at (1, 0) meters Ep = kQ/r^2 = (9E9)(4E-9)/1^2 = 36N/C F = qE. Force on charge q = 2nC at P is: F = (2E-9)(36N/C) = 72E-9 N in +x dir. Force on charge q = -2nC at P is: F = (2E-9)(36N/C) = 72E-9 N in -x dir.

16. 16 Field Example: Q = +8nC at (0, 0), “P” at (2, 0) meters

17. Calculating E for 2 or more Point Charges 1.Calc. distance from each charge to “P” 2.Calc. size of each field at P 3.Calc. sine & cosine for each direction 4.Calc. x,y components of each field 5.Add x,y components separately 6.Convert x,y to E,  (polar coords.)

18. 18 Component Example: +1nC at (4, 3) meters, “P” at origin

19. 19 15 Summary charge is quantized & conserved due to protons and electrons conductivity depends on availability of free electrons Coulomb’s law describes forces field E = F/q force and field are vector sums