Units of Chapter 15 Electric Charge Electrostatic Charging

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

Electric Charge • • Transferred (not destroyed) Symbol: q, Q [coulomb, C] Q = ±Ne (N = integer, e = 1. 6 E-19 C) Like repel, Unlike attract, with force ~ 1/distance 2 • Atom (Wilson) • / 2

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

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 • / 4

Coulomb’s Law ke = 9. 0 x 109 N m 2/C 2. q 1 r q 2 5

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

Example - + • -1 nanocoulomb charge at origin, +1 nanocoulomb charge is at x = 1 meter. • force = 9 E 9(1 E-9)/1 x 1 = 9 E-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? 7

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 //// 8

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

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 / 10

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 11

Electric Field Demo • In oil • http: //video. google. com/videoplay? docid=879375962512 6360449&ei=b. Tb. BSLa. CEYrgw. HE 57 Xo. CQ&q=electric+field+lines&vt=lf&hl=en • On a flame: • http: //www. youtube. com/watch? v=MPFkp 2 Hr. Ecs

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 = k. Qq/r 2. • field E = F/q = (k. Qq/r 2)/q = k. Q/r 2. • field around Q does not depend on q. • E is outward if Q is +, inward if Q is - // 13

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 14

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

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

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

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

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 19