Transcript Document
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 = 1.6E-19 C) Like repel, Unlike attract, with force ~ 1/distance2 • Atom (Wilson) • / 2 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 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 q1q2 F ke 2 r ke = 9.0 x 109 N m2/C2 . q1 r q2 5 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 //// 6 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? 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) 10nC is at (0, 0.5) meters 2) -5nC is at (0.5, 0) meters Calculate force on 1nC at (0, 0). 9 9 kQ1q (9 10 )(10 10 )(110 ) 9 F1 2 360 10 N 2 r 0.5 kQ2 q (9 109 )(5 109 )(1109 ) 9 F2 2 180 10 N 2 r 0.5 9 Force = 180nN Right + 360nN 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=bTbBSLaCEYrgwHE57XoCQ&q=electric+field+lines&vt=lf&hl=en • On a flame: • http://www.youtube.com/watch?v=MPFkp2 HrEcs 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/r2. • field E = F/q = (kQq/r2)/q = kQ/r2. • 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 = +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. 15 Field Example: Q = +8nC at (0, 0), “P” at (2, 0) meters r x 2 y 2 22 02 4 2 kQ (9 E 9)(8E 9) EQ 2 18 N / C 2 r 2 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.) E E E 2 x 2 y Ey q tan Ex 1 Component Example: +1nC at (4, 3) meters, “P” at origin r x 2 y 2 42 32 25 5 cosq x / r 4 / 5 sin q y / r 3 / 5 EQx kQ 9 4 2 cos q 0.288 N / C r 25 5 EQ y kQ 9 3 2 sin q 0.216 N / C r 25 5 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