Electic Chage Fom Last Time Two types: plus and minus Foces between chages Like chages epel, opposite chages attact Coulomb s law: foce dops invesely w/ squae of distance Electic Cuent Flow of chages fom Coulomb foce Can geneate spak jumping though ai Wed. Feb 27, 2006 Phy107 Lectue 16 1 paks epaate enough chage, stong Coulomb foces tea electons fom ai atoms Chaged paticles flow fom one electode to the othe This flow of chaged paticles is an electic cuent. Wed. Feb 27, 2006 Phy107 Lectue 16 2 Othe electic cuents Battey moves electical chage at constant ate Exets a foce on the paticles Battey voltage is like potential enegy Volts Timevaying electic cuent Timevaying cuents (nonconstant speed paticles) can poduce an EM wave. E.g. a spak As spak jumps gap, chaged paticles stat flowing then stop. e electon Wok done = change in kinetic enegy = (foce) x (distance) = (chage) x (voltage) Wed. Feb 27, 2006 Phy107 Lectue 16 3 Wed. Feb 27, 2006 Phy107 Lectue 16 4 Eventually tansatlantic signals! Induction coils Capacito banks pak gap A Tansvese wave. Electic/magnetic fields pependicula to popagation diection Can tavel in empty space f = v/λ, v = c = 3 x 10 8 m/s (186,000 miles/second!) Gulgielmo Maconi s tansatlantic tansmitte Wed. Feb 27, 2006 Phy107 Lectue 16 5 Wed. Feb 27, 2006 Phy107 Lectue 16 6 1
The idea of electic fields The electic field EM wave made up of oscillating electic and magnetic fields. But what is an electic field? Electic field is a way to descibe the foce on a chaged paticle due to othe chages aound it. Foce = chage electic field The diection of the foce is the diection of the electic field. Foce on this chage Q 2 Q 1 due to this chage F = k Q 1Q 2 2 Foce = ( Chage) " ( Electic field) Wed. Feb 27, 2006 Phy107 Lectue 16 7 Wed. Feb 27, 2006 Phy107 Lectue 16 8 Question Which vecto best epesents the foce on a (positively chaged) test paticle at the ed dot? (Think supeposition!) A. A A B. B C. C D. D E. E B C D E Visualizing the electic field Faaday invented the idea of field lines following the foce to visualize the electic field. Local electic field is same diection as field lines. Foce is paallel o antipaallel to field lines. Chaged paticle will move along these field lines. Field lines emanate fom positive chage and teminate on negative chage. Wed. Feb 27, 2006 Phy107 Lectue 16 9 Wed. Feb 27, 2006 Phy107 Lectue 16 10 Why bothe? Why invent fields why not just use foces? Think of the EM wave. A spak is an acceleating cuent flow, poducing the wave. The wave continues to popagate even when the spak is gone. o chages anywhee, but timevaying fields popagate as a wave. Electic field: summay Electic field > will be a foce on a chaged paticle. This foce ( and electic field) can aise fom electic chages (via Coulomb s law) But once electic field is known, don t need to know the chages that poduce it. Wed. Feb 27, 2006 Phy107 Lectue 16 11 Wed. Feb 27, 2006 Phy107 Lectue 16 12 2
Magnets Clealy magnets inteact with each othe ometimes attacting, sometimes epelling But the magnetic paticles ae sot of a composite positive and negative magnetic chage. Visualized as a ba with positive pole (oth) at one end and negative pole (outh) at othe. These magnetic chages cannot be boken apat always appea in pais. Magnetism: Pemanent magnets oth Pole and outh Pole This is the elementay magnetic paticle Called magnetic dipole (oth pole and outh pole) Poles inteact with each othe simila to chages. Opposites attact Likes epel Wed. Feb 27, 2006 Phy107 Lectue 16 13 Wed. Feb 27, 2006 Phy107 Lectue 16 14 Alignment foce Magnetic field But eally one of the magnets is tying to align the othe one. Which way will these magnets tend to align? A B C D imila in spiit to electic field Used to detemine oientational foce on a compass needle: Magnetic field exets a foce on compass needle Aligns it with magnetic field lines. Magnetic field lines indicate diection of local magnetic field tat at pole, end at pole Wed. Feb 27, 2006 Phy107 Lectue 16 15 Wed. Feb 27, 2006 Phy107 Lectue 16 16 The Eath is a magnet! Eath is a ba magnet. oth magnetic pole ~ at south geogaphic pole A compass is a ba magnet upise! Electic cuent poduces magnetic field Cuent (flow of electic chages ) in wie poduces magnetic field. That magnetic field aligns compass needle Cuent Compass needle aligns with local Eath field Wed. Feb 27, 2006 Phy107 Lectue 16 17 Magnetic field Wed. Feb 27, 2006 Phy107 Lectue 16 18 3
Magnetic field fom a cuent Magnetic foce on electic chages Effect of unifom Bfield on chaged paticle Chaged paticle not moving no effect Chaged paticle is moving: foce exeted pependicula to both field and velocity Ion filings align with magnetic field lines Magnetic field loops aound the cuent. Wed. Feb 27, 2006 Phy107 Lectue 16 19 Wed. Feb 27, 2006 Phy107 Lectue 16 20 Magnetic Foce on a Cuent I Homopola moto Why does the moto tun? Cuent Foce on each moving chage Chages tapped in wie > foce on wie when cuent is flowing Magnetic field Magnetic foce Wed. Feb 27, 2006 Phy107 Lectue 16 21 A. Electic Coulomb foce pushes on magnet B. Magnetic field pushes on cuent fom battey C. Cuent fom battey heats the magnet D. Cuent though wie poduces magnetic field Wed. Feb 27, 2006 Phy107 Lectue 16 22 Foces between cuents Which of these pais of cuents will attact each othe? A. A B. A & C C. B A B C Timevaying magnetic field Up to this point, electic and magnetic fields constant in time Constant electic cuent poduces constant magnetic field. Constant magnetic field poduces nothing in paticula! But changing the magnetic field in time poduces an electic field! This effect is called induction. Wed. Feb 27, 2006 Phy107 Lectue 16 23 Wed. Feb 27, 2006 Phy107 Lectue 16 24 4
Faaday s law of induction Faaday s law: timevaying magnetic field poduces electic field tength of electic field popotional to how fast magnetic field changes. In this expeiment: Magnetic field is lagest close to the ba magnet, dops off fathe away. Moving magnet towad coil causes magnetic field though coil to incease with time, poducing electic field ince coil is conducting, this electic field poduces a cuent in the wie of the coil and though the mete. Wed. Feb 27, 2006 Phy107 Lectue 16 25 One step futhe: Lenz s law This induced cuent poduces a magnetic field, which inteacts with the ba magnet just as anothe ba magnet would. Lenz s law descibes the diection of the induced field (o equivalently, the diection of the induced cuents) The induced cuent ciculates in such a way as to geneate a magnetic field that tends to cancel the change in the field. Causes epulsive foce on oiginal moving ba magnet. Wed. Feb 27, 2006 Phy107 Lectue 16 26 Timevaying electic field What diection foce do I feel due to Lenz law when I push the magnet down?? A. Up B. Down C. Left D. Right Coppe tong magnet Can also poduce a timevaying magnetic field with a timevaying cuent in an electomagnet. Faaday s law: timevaying magnetic field poduces electic field, electic field poduces electic cuent (in a metal). Just as befoe, the cuent is induced in such a way that the esulting magnetic dipole epels the changing flux that poduced the cuent. This is the pinciple of an electomagnetic gun. Wed. Feb 27, 2006 Phy107 Lectue 16 27 Wed. Feb 27, 2006 Phy107 Lectue 16 28 Maxwell s unification Intimate connection between electicity and magnetism Timevaying magnetic field induces an electic field (Faaday s Law) Timevaying electic field geneates a magnetic field " # E = $ 1 % B c %t In vacuum: " # B = 1 c % E %t This is the basis of Maxwell s unification of electicity and magnetism into Electomagnetism Electomagnetic Waves Cuent (up and down) ceates electomagnetic wave oscillating electic and magnetic fields Wed. Feb 27, 2006 Phy107 Lectue 16 29 Wed. Feb 27, 2006 Phy107 Lectue 16 30 5