Eventually transatlantic signals! From Last Time. Electromagnetic Waves. The idea of electric fields. The electric field.

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1 Fom Last Time Electomagnetic waves Chages, cuent and foces: Coulomb s law. Acceleating chages poduce an electomagnetic wave The idea of the electic field. Today Electic fields, magnetic fields, and thei unification Eventually tansatlantic signals! Induction coils Capacito banks pak gap Gulgielmo Maconi s tansatlantic tansmitte Mon. Feb 20, 2006 Phy107 Lectue 14 1 Mon. Feb 20, 2006 Phy107 Lectue 14 2 Electomagnetic Waves A Tansvese wave. Electic and magnetic fields ae pependicula to popagation diection Can tavel in empty space f = v/λ v = c = 3 x 10 8 m/s (186,000 miles/second!) z y x The idea of electic fields 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. Mon. Feb 20, 2006 Phy107 Lectue 14 3 Mon. Feb 20, 2006 Phy107 Lectue 14 4 Question The electic field Diection of foce between two paticles of the same chage (use next slide). Foce on this chage Q 2 Q 1 due to this chage F = k Q 1Q 2 2 Foce = ( Chage) " ( Electic field) Mon. Feb 20, 2006 Phy107 Lectue 14 5 Mon. Feb 20, 2006 Phy107 Lectue

2 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. 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 time-vaying fields popagate as a wave. Mon. Feb 20, 2006 Phy107 Lectue 14 7 Mon. Feb 20, 2006 Phy107 Lectue 14 8 Electic field: summay Pesence of electic field means that thee will be a foce on a chaged paticle. This foce ( and electic field) can aise fom electic chages (via Coulomb s law) Is a way to detemine foces on a chaged paticle without thinking about the chages that give ise to the foces. But wait thee s moe Enegy can be stoed in the field. Enegy density popotional to (Electic field) 2 (Magnetic field) 2 Electomagnetic foces aen t felt instantaneously, the popagate at speed of electomagnetic wave (speed of light) Object tansfes momentum to the field, which late tansfes it to anothe object. Mon. Feb 20, 2006 Phy107 Lectue 14 9 Mon. Feb 20, 2006 Phy107 Lectue Magnetic foces Magnetism: Pemanent 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. oth Pole and outh Pole This is the elementay magnetic paticle Called magnetic dipole (oth pole and outh pole) Opposites attact Likes epel These magnetic chages cannot be boken apat always appea in - pais. Poles inteact with each othe simila to chages. Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue

3 Magnetic field imila in spiit to electic field Used to detemine the oientational foce on a magnetic dipole: Magnetic field exets a foce on a dipole that aligns it with magnetic field lines. Unifom magnetic field only otates dipole: doesn t cause it to move. tatic magnetic field aises fom pemanent magnets (o cuents). But, as electic field, can exist in an EM wave even without magnetic dipoles. Field lines of a magnet Field lines indicate diection of field Density indicates stength of field imila to electostatic foce, but foce is felt by magnetic dipole Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue The Eath is a magnet! Eath is a magnetic dipole. oth magnetic pole ~ at south geogaphic pole A compass is a magnetic dipole 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 Mon. Feb 20, 2006 Phy107 Lectue Magnetic field Mon. Feb 20, 2006 Phy107 Lectue Magnetic field fom a cuent Foces between cuents Which of these pais of cuents will attact each othe? A. A B. A & C C. B Ion filings align with magnetic field lines Magnetic field loops aound the cuent. A B C Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue

4 Magnetic field fom a cuent loop One loop: field still loops aound the wie. Many loops: same effect olenoid electomagnet equence of cuent loops can poduce stong magnetic fields. This is an electomagnet Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue upeconducting Magnets olenoid as in conventional electomagnet. But once cuent is injected, powe supply tuned off, cuent and magnetic field stays foeve as long as T < T c Mon. Feb 20, 2006 Phy107 Lectue Magnetic Field Ranges Field ize Example Field ize Example 850 T 60 T 33 T 2 T 0.5 T 0.4 T 0.2 T 0.01 T T T 3x10-10 T Mon. Feb 20, 2006 Phy107 Lectue Magnets fo MRI Lage scale applications Magnetic Resonance Imaging typically done at 1.5 T upeconducting magnet to povides static magnetic field patial esolution of positions of tace atomic nuclei. upeconducting magnet Plasma confinement tous Poposed ITER fusion test eacto Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue

5 Time-vaying 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. Mon. Feb 20, 2006 Phy107 Lectue Faaday s law of induction Faaday s law: time-vaying 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. Mon. Feb 20, 2006 Phy107 Lectue 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. Time-vaying electic field Can also poduce a time-vaying magnetic field with a time-vaying cuent in an electomagnet. Faaday s law: time-vaying 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. Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue Maxwell s unification Intimate connection between electicity and magnetism Time-vaying magnetic field induces an electic field (Faaday s Law) Time-vaying 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 consisting of oscillating electic and magnetic fields - Mon. Feb 20, 2006 Phy107 Lectue Mon. Feb 20, 2006 Phy107 Lectue

6 Electomagnetic Waves y z x A Tansvese wave. Electic and magnetic fields ae pependicula to popagation diection Can tavel in empty space f = v/λ v = c = 3 x 10 8 m/s (186,000 miles/second!) Mon. Feb 20, 2006 Phy107 Lectue