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Today: Electromagnetic waves, electricity and magnetism From last time… • Interference of waves – Constructive interference – Destructive interference • • • • • Doppler effect – Change in apparent frequency due to motion of source or observer – Lorenz force on moving charged particle – Faraday induction of currents by changing magnetic field. • Resonance – Natural frequency of oscillation – Object will tend to oscillate at that frequency – Other frequencies (wavelengths) cancelled by destructive interference reflections Fri. Feb 17, 2006 Phy107 Lecture 13 Electromagnetic waves Electric charge and electric forces Magnetic forces Unification of electric and magnetic forces 1 Fri. Feb 17, 2006 Phy107 Lecture 13 2 Properties of EM Waves Electromagnetic (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. 1865: James Clerk Maxwell published mathematical theory relating electricity and magnetism Predicted electromagnetic waves Fri. Feb 17, 2006 1887: Heinrich Hertz produced and measured electromagnetic waves in the laboratory. Phy107 Lecture 13 3 • Electric and magnetic fields are perpendicular to propagation direction: a transverse wave. • Propagation speed c = 3 x 108 m/s (186,000 miles/second!) Fri. Feb 17, 2006 Phy107 Lecture 13 4 Sizes of EM waves • Visible light has a typical wavelength of 500 nm = 500 x 10-9 m = 0.5 x 10-6 m = 0.5 microns (µm) Types of EM waves • A human hair is roughly 50 µm diameter We are familiar with many different wavelengths of EM waves – 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 All are the same phenomena Fri. Feb 17, 2006 • AM 1310, your badger radio network, has a vibration frequency of 1310 KHz = 1.31 MHz Phy107 Lecture 13 5 Fri. Feb 17, 2006 Phy107 Lecture 13 6 1 Question Electric and magnetic fields AM 1310, your badger radio network, has a vibration frequency of 1310 KHz = 1310 x 103 Hz = 1.31 x 106 Hz It travels at 3 x 108 m / s. What is it’s wavelength? • To understand electric and magnetic fields, need to take a few steps back. • Probably familiar with electrostatic shocks A. 230 meters B. 2.3 meters C. 0.0043 meters D. 4.3 meters Fri. Feb 17, 2006 • But what are electric, magnetic fields? • This comes from electric charge • We now know that there are two varieties of electric charge, positive and negative. Phy107 Lecture 13 7 Fri. Feb 17, 2006 Phy107 Lecture 13 8 Pos and neg charges can be separated Electrical Charge • Triboelectric • Only the negative charge moves around. These are the electrons. – Charge is transferred as a result of mechanical (frictional) action • The positive charges are protons. Protons and electrons form a ‘planetary’ atom. • Conduction – • Electrons orbit around a nucleus containing the protons. Compare planets orbiting around a sun. – charge transfer by contact (spark) • Atoms are bound together, forming solid materials. Electrons can be torn from atoms, transferred to other materials. Fri. Feb 17, 2006 Phy107 Lecture 13 9 Fri. Feb 17, 2006 Phy107 Lecture 13 10 Separating charge Electrical charge Rod becomes positively charged after rubbing with fur. • Electrons carry electrical charge, and can be moved 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 charge Electrons (negative charges) have been transferred from rod to fur. Charge on 1 electron = 1.6 x 10-19 Coulomb • Positively charged rod can then be used to transfer electrons from other objects. Transferring 1 Coulomb of charge means that 6,250,000,000,000,000,000 electrons have moved! Fri. Feb 17, 2006 Phy107 Lecture 13 11 Fri. Feb 17, 2006 Phy107 Lecture 13 12 2 Charge by conduction (touching) +- + - -+ + - + + + + + + + + + + + ++ Positively charged rod (too few electrons) + + + + + + + + + + ++ electron flow + + + + Less positively charged rod Fri. Feb 17, 2006 Why did the electrons flow? Neutral metal Phy107 Lecture 13 attractive force between positive and negative charges. repulsive force between two positive or two negative charge +-+ - -+ + - + The positively charged rod attracts negative charges to the top of the electroscope. This leaves positive charges on the leaves. + + + + + + + + Interactions between charges Positively charged metal Pith ball 13 demo The like-charges on the leaves repel each other. Fri. Feb 17, 2006 Phy107 Lecture 13 Force between charges 14 Question + Opposite charges attract Force on positive particle due to negative particle Like charges repel. • Other than the polarity, they interact much like masses interact gravitationally. • Force is along the line joining the — particles. The force between two electrons is 10-10. The distance between the electrons is doubled. The force is now A. B. C. D. Electrostatic force: FE = k Q1 Q 2 /r2 k = 9x109 Nm2/C2 Gravitational force: FG=GM1M 2/ r2 0.5 x 10-10 N 0.25 x 10-10 N 1 x 10-10 N 2 x 10-10 N G=6.7x10-11 Nm2/kg2 Fri. Feb 17, 2006 Phy107 Lecture 13 15 Fri. Feb 17, 2006 • Electrostatic force between proton and electron in a hydrogen atom + F 16 Electrical machines Electrostatic force is strong Qp=1.6x10-19 C Phy107 Lecture 13 Qe = -1.6x10-19 C - r = 1x10-10 m FE = (9x109)(1.6x10-19)(1.6x10-19)/(10-10)2 = 2.3x10-8 N • Can mechanize the rubbing process to continually separate charge. • This charge can then be transferred to other objects. • Gravitational force between proton and electron FG = (6.7x10-11)(1.7x10-27)(9.1x10-31)/(10-10) 2 = 2.3x10-28 N Fri. Feb 17, 2006 Phy107 Lecture 13 17 Fri. Feb 17, 2006 Phy107 Lecture 13 18 3 The van de Graf machine Charge transfer and forces + + + + - - + + + + • Ben Franklin’s ‘door bell’. • Announced presence of lightning so knew to go out and do his experiments! Fri. Feb 17, 2006 Phy107 Lecture 13 19 • The van de Graf machine continually transfers charge to the ‘dome’ via a moving belt. • Charge on the dome can be transferred to other objects. Fri. Feb 17, 2006 Phy107 Lecture 13 20 Sparks Van de Graaf The sphere gives the girl a large negative charge. Each strand of hair is trying to: A. Get away from the charged sphere. B. Get away from the ground. C. Get away from the other strands of hair. • If we separate enough charge, strong attractive/repulsive forces can tear electrons from air atoms • Charged particles flow from one electrode to the other • This flow of charged particles is an electric current. Like charges attached to the hair strands repel, causing them to get away from each other. Fri. Feb 17, 2006 Phy107 Lecture 13 21 Fri. Feb 17, 2006 Producing EM Waves Phy107 Lecture 13 22 Hertz wave generator Accelerating electrical current generates a wave that travels through space. Lightning / spark produces electromagnetic wave. Wave consists of oscillating electric and magnetic fields. But still haven’t said what electric/magnetic fields are + Fri. Feb 17, 2006 Phy107 Lecture 13 23 Fri. Feb 17, 2006 Phy107 Lecture 13 24 4 Resonators again! Eventually transatlantic signals! Capacitor banks Induction coils Spark gap • Transmitter Transmitter Receiver The balls and rods formed an electrically resonant circuit Resonantly tuned to pick up the transmitted signal Spark initiated oscillations at resonant freuquency ~ 1 MHz Fri. Feb 17, 2006 Phy107 Lecture 13 25 Gulgielmo Marconi’s transatlantic transmitter Fri. Feb 17, 2006 The idea of electric fields Phy107 Lecture 13 26 Why bother? • EM wave made up of oscillating electric and magnetic fields. • Why invent fields - why not just use forces? • But what is an electric field? • Think of the EM wave. A spark is an accelerating current flow, producing the wave. • Electric field is a way to describe the force on a charged particle due to other charges around it. • The wave continues to propagate even when the spark is gone. • Force = charge × electric field • No charges anywhere, but oscillating fields are still present. • The direction of the force is the direction of the electric field. • This is an extension of the basic idea of fields. Fri. Feb 17, 2006 Phy107 Lecture 13 27 Fri. Feb 17, 2006 Phy107 Lecture 13 28 Electric field lines • Faraday invented the idea of field lines following the force to visualize the electric field. Field lines emanate from positive charge and terminate on negative charge. Local electric field is same direction as field lines. Force is parallel or antiparallel to field lines. Charged particle will move along these field lines. Fri. Feb 17, 2006 Phy107 Lecture 13 29 5