1Wed. Feb 27, 2006 Phy107 Lecture 161From Last Time…• Magnets, magnetic forces– North and South poles– Mag. Fields tend to align other magnets• Time-varying fields– Time varying magnetic field produces electricfield– Time-varying electric field produces magneticfieldWed. Feb 27, 2006 Phy107 Lecture 162Time-varying fieldsTime-varying magnetic field generateselectric fieldCopperStrong magnet…and a time-varying electric field producesa magnetic fieldWed. Feb 27, 2006 Phy107 Lecture 163Maxwell’s unification• Intimate connectionbetween electricity and magnetism• Time-varying magnetic fieldinduces an electric field (Faraday’s Law)• Time-varying electric field generates amagnetic fieldThis is the basis of Maxwell’s unification ofelectricity and magnetism into Electromagnetism ! r " #r E = $1c%r B %tr " #r B = 1c%r E %tIn vacuum:Wed. Feb 27, 2006 Phy107 Lecture 164+- Electromagnetic WavesCurrent (up and down)creates electromagnetic waveoscillating electric and magnetic fieldsWed. Feb 27, 2006 Phy107 Lecture 165Electromagnetic Wavesxzy• A Transverse wave.• Electric and magnetic fields are perpendicular topropagation direction• Different from ‘mechanical wave’.•Needs no medium to propagateMaxwell’s eqns predict that wave propagates at‘speed of light’, cWed. Feb 27, 2006 Phy107 Lecture 166What about electromagnetism?• Maxwell equations say that– Light moves at constant speed c=3x108 m/sec in vacuum• But can this be right?– Jane would expect to see light pulse propagate at c+v– But Maxwell says it should propagate at c, if physics is the same forJoe and Jane.– If it is different for Joe and Jane, then which one measures c?JaneJoe2Wed. Feb 27, 2006 Phy107 Lecture 167MovingchargesMoving charge is an electric current, current producesmagnetic fieldJoe and Jane both have compass needles.JaneJoeA. Both needles deflectB. Neither needle deflectsC. Jane’s needle deflects, but Joe’s does notWed. Feb 27, 2006 Phy107 Lecture 168Special Relativity• From 1905 to 1908,Einstein developed specialtheory of relativity.• Completely different idea oftime and space.• Everything relative.No absolute lengths, times,energies.Our usual conceptions of space and time are at best misguided.Wed. Feb 27, 2006 Phy107 Lecture 169Frames of reference• Frame of reference:– The coordinate system in which you observe events.– e.g. The room around you.– You judge how fast a thrown ball goes by its velocityrelative to some stationary object in the room.– You judge how high athrown ball goes by distancefrom the floor, ceiling, etc.– You judge how fast you aremoving by looking at objectsaround youWed. Feb 27, 2006 Phy107 Lecture 1610Which reference frameSuppose you are on the bus to Chicago driving at 60 mph,and throw a ball forwards at 40 mph.From your seat on the bus,the speed of ball is the same as in this classroom.To the major league scout on the side of the road,your 40 mph throw has become a 100 mph fastball.Who is correct?You wouldn’t last long in the majors.The important velocity in a baseball game isthe relative velocity of ball with respect topitcher or the batter.Wed. Feb 27, 2006 Phy107 Lecture 1611• Earth spins on its axis– One rotation in (24 hrs)(60 min/hr)(60 sec/min)=86400 sec– Point on surface moves 2πRE in one rotation.– Surface velocity = 2π(6.4x106 m)/86400 sec = 465 m/s• Earth revolves around sun– One revolution in (365 days)(86400 sec/day)=3.15x107 sec– Earth velocity = 2π(1.5x1011 m)/ 3.15x107 sec=3x104 m/s• Sun moves w/ respect to center of our galaxy– Sun velocity = 2.3x105 m/s But what exactly is the absolute velocity of the ball?Wed. Feb 27, 2006 Phy107 Lecture 1612Galilean relativity• Absolute velocity not clear, but we canseemingly agree on relative velocities.– In all cases the ball moves 40 mph faster than I do.• Examples of two different reference frames– On the bus– Off the bus• In both cases we could talk about– the forces I put on the ball,– the acceleration of the ball, etc3Wed. Feb 27, 2006 Phy107 Lecture 1613Newton’s laws in moving frames• In both cases,the acceleration of the ball is the same.• This is because the two reference frames move at aconstant relative velocity.• Newton’s laws hold for each observer.• Which is good, because we apparently can’tdetermine our absolute velocity,or even if we are moving at all!This is an example of Galilean RelativityWed. Feb 27, 2006 Phy107 Lecture 1614Example of Galilean relativity• Observer on ground• Observer in plane• Experiment may look differentto different observers, but bothagree that Newton’s laws hold– Can make observations agreeby incorporating relativevelocities of frames.Wed. Feb 27, 2006 Phy107 Lecture 1615Galilean relativity: example• Experiment performed…– in laboratory at rest with respect to earth’s surface– in airplane moving at constant velocity…must give the same result.v=0v>0• In both cases, ball is observed to rise up and returnto thrower’s hand– Process measured to take same time in both experiments– Newton’s laws can be used to calculate motion in both.Wed. Feb 27, 2006 Phy107 Lecture 1616Some other examples• On an airplane:– Pouring your tomato juice.– Throwing peanuts pretzel sticks into your mouth.– But when the ride gets bumpy…• In a car:– Drinking coffee on a straight, smooth road– But accelerating from a light,or going around a curveWed. Feb 27, 2006 Phy107 Lecture 1617Turning this around…• No experiment using the laws of mechanics candetermine if a frame of reference is moving atzero velocity or at a constant velocity.• Concept of absolute motion is not meaningful.– There is no ‘preferred’ reference frameInertial Frame: reference frame moving in straight line with constant speed.Wed. Feb 27, 2006 Phy107 Lecture 1618QuestionYou riding in a car at 30 mph, and you throw a balldirectly backwards at 20 mph just as you pass astationary observer. The observer seesA. Ball drops directly to the ground with nohorizontal motionB. Ball moves backwards at 20 mph and fallsC. Ball moves forwards at 10 mph and falls to ground.4Wed. Feb 27, 2006 Phy107 Lecture 1619QuestionYou riding in a car at 30 mph, and you throw a balldirectly backwards at 30 mph just as you pass astationary observer. The observer seesA. Ball drops directly to the ground with no horizontal motionB. Ball moves backwards at 30 mph and fallsC. Ball moves forwards at
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