1Mon. Feb 26, 2006 Phy107 Lecture 151From last time…• Interference of waves– Constructive interference– Destructive interference• Doppler effect– Change in apparent frequency due to motionof source or observer• Resonance– Natural frequency of oscillation– Object will tend to oscillate at that frequency– Other frequencies (wavelengths) cancelled bydestructive interference reflectionsMon. Feb 26, 2006 Phy107 Lecture 152Today: Electromagnetic waves,electricity and magnetism• Electromagnetic waves• Electric charge and electric forces• Magnetic forces• Unification of electric and magnetic forces– Lorenz force on moving charged particle– Faraday induction of currents by changingmagnetic field.Mon. Feb 26, 2006 Phy107 Lecture 153Electromagnetic (EM) waves1865: James Clerk Maxwellpublished mathematical theoryrelating electricity and magnetismPredicted electromagnetic waves1887: Heinrich Hertzproduced and measuredelectromagnetic waves in thelaboratory.Mon. Feb 26, 2006 Phy107 Lecture 154Properties of EM Waves• Has all properties of a wave: wavelength, frequency, speed• At a fixed location,electric and magnetic fields oscillate in time.• Electric and magnetic fields in the wave propagate in empty space at the wave speed.• Electric and magnetic fields are perpendicular topropagation direction: a transverse wave.• Propagation speed c = 3 x 108 m/s (186,000 miles/second!)Mon. Feb 26, 2006 Phy107 Lecture 155Types of EMwavesWe arefamiliarwith manydifferentwavelengthsof EM wavesAll are thesamephenomenaMon. Feb 26, 2006 Phy107 Lecture 156Sizes of EM waves• Visible light has a typical wavelength of500 nm = 500 x 10-9 m = 0.5 x 10-6 m= 0.5 microns (µm)• A human hair is roughly 50 µm diameter– 100 wavelengths of visible light fit in human hair• A typical AM radio wave has a wavelength of 300 meters!• It’s vibration frequency is f = c / λ= 3x108 m/s / 300 m = 1,000,000 cycles/s = 1 MHz• AM 1310, your badger radio network,has a vibration frequency of 1310 KHz = 1.31 MHz2Mon. Feb 26, 2006 Phy107 Lecture 157QuestionAM 1310, your badger radio network, has a vibrationfrequency of 1310 KHz = 1310 x 103 Hz = 1.31 x 106 HzIt travels at 3 x 108 m / s.What is it’s wavelength?A. 230 metersB. 2.3 metersC. 0.0043 metersD. 4.3 metersMon. Feb 26, 2006 Phy107 Lecture 158Electric and magnetic fields• But what are electric, magnetic fields?• To understand electric and magnetic fields,need to take a few steps back.• Probably familiar with electrostatic shocks• This comes from electric charge• We now know that there are two varieties ofelectric charge, positive and negative.Mon. Feb 26, 2006 Phy107 Lecture 159Electrical Charge• Only the negative charge moves around.These are the electrons.• The positive charges are protons.Protons and electrons form a ‘planetary’ atom.• Electrons orbit around a nucleus containing the protons.Compare planets orbiting around a sun.• Atoms are bound together, forming solid materials.Electrons can be torn from atoms,transferred to other materials.Mon. Feb 26, 2006 Phy107 Lecture 1510Pos and neg charges can beseparated• Triboelectric– Charge is transferred as a result of mechanical(frictional) action• Conduction –– charge transfer by contact (spark)Mon. Feb 26, 2006 Phy107 Lecture 1511Electrical charge• Electrons carry electrical charge, and can bemoved from one material to another.• The electrons have a negative charge.• The unit of electric charge is the Coulomb• One electron carries only a tiny amount of chargeCharge on 1 electron = 1.6 x 10-19 CoulombTransferring 1 Coulomb of charge means that6,250,000,000,000,000,000 electrons have moved!Mon. Feb 26, 2006 Phy107 Lecture 1512Separating charge• Positively charged rod can then be used totransfer electrons from other objects.Rod becomespositively chargedafter rubbing with fur.Electrons (negativecharges) have beentransferred from rodto fur.3Mon. Feb 26, 2006 Phy107 Lecture 1513Sign of ChargeCharges of the same sign repel one another andcharges with opposite signs attract one anotherMon. Feb 26, 2006 Phy107 Lecture 1514Charge by conduction (touching)Neutralmetal+++++++++++++++++-----Positively charged rod(too few electrons)+++++++Less positively charged rod+++++Positivelychargedmetal+++++++++++++++++-----electron flowPith ball demoMon. Feb 26, 2006 Phy107 Lecture 1515ElectroscopeThe positively charged rod attractsnegative charges to the top of theelectroscope.This leaves positive charges on theleaves.The like-charges on the leaves repeleach other.Mon. Feb 26, 2006 Phy107 Lecture 1516Quick QuizA negatively charged rod is used to charge an electroscopeby induction. What is the resulting net charge on theelectroscope leaves?A. Positive.B. Zero.C. Negative.If negative charged rod were used, negative charges from thetop of the electroscope are repelled and drift to the leaves whichend up with a net negative charge, while the top of theelectroscope is positive.Mon. Feb 26, 2006 Phy107 Lecture 1517Interactions between chargesThe positively charged rod attracts negativecharges to the top of the electroscope.This leaves positive charges on the leaves.The like-charges on the leaves repel eachother.attractive force between positive andnegative charges.repulsive force between two positiveor two negative chargeWhy did the electrons flow?Mon. Feb 26, 2006 Phy107 Lecture 1518Force between chargesOpposite charges attractLike charges repel.• Other than the polarity, they interactmuch like masses interact gravitationally.• Force is along the line joining theparticles.Gravitational force: FG=GM1M2/ r2G=6.7x10-11 Nm2/kg2Electrostatic force: FE = k Q1 Q2 /r2k = 9x109 Nm2/C2+—Force on positive particledue to negative particle4Mon. Feb 26, 2006 Phy107 Lecture 1519QuestionThe force between two electrons is 10-10 N.The distance between the electrons isdoubled. The force is nowA. 0.5 x 10-10 NB. 0.25 x 10-10 NC. 1 x 10-10 ND. 2 x 10-10 NMon. Feb 26, 2006 Phy107 Lecture 1520Electrostatic force is strong• Electrostatic force between proton and electronin a hydrogen atomFG = (6.7x10-11)(1.7x10-27)(9.1x10-31)/(10-10)2 = 2.3x10-28 N+ -r = 1x10-10 mQp=1.6x10-19 C Qe = -1.6x10-19 CF• Gravitational force between proton and electronFE = (9x109)(1.6x10-19)(1.6x10-19)/(10-10)2 = 2.3x10-8 NMon. Feb 26, 2006 Phy107 Lecture 1521Electrical machines• Can mechanize therubbing process tocontinually separatecharge.• This charge can thenbe transferred toother
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