1Wed. Feb 27, 2006 Phy107 Lecture 161From Last Time…• Electric Charge– Two types: plus and minus• Forces between charges– Like charges repel, opposite charges attract– Coulomb’s law:force drops inversely w/ square of distance• Electric Current– Flow of charges from Coulomb force– Can generate spark jumping through airWed. Feb 27, 2006 Phy107 Lecture 162Sparks• Separate enough charge,strong Coulomb forces tear electrons from air atoms• Charged particles flow from one electrode to the other• This flow of charged particles is an electric current.Wed. Feb 27, 2006 Phy107 Lecture 163Other electric currents• Battery moves electrical charge at constant rate• Exerts a force on the particles• Battery voltage is like potential energyWork done =change in kinetic energy= (force) x (distance)= (charge) x (voltage)-eVoltselectronWed. Feb 27, 2006 Phy107 Lecture 164Time-varying electric current• Time-varying currents (non-constant speedparticles) can produce an EM wave.• E.g. a spark• As spark jumps gap, charged particles startflowing then stop.Wed. Feb 27, 2006 Phy107 Lecture 165• A Transverse wave.• Electric/magnetic fields perpendicular topropagation direction• Can travel in empty spacef = v/λ, v = c = 3 x 108 m/s (186,000 miles/second!)Wed. Feb 27, 2006 Phy107 Lecture 166Eventually transatlantic signals!Gulgielmo Marconi’s transatlantic transmitterCapacitorbanksInductioncoilsSpark gap2Wed. Feb 27, 2006 Phy107 Lecture 167The idea of electric fields• EM wave made up ofoscillating electric and magnetic fields.• But what is an electric field?• Electric field is a way to describe the forceon a charged particle due to other chargesaround it.• Force = charge × electric field• The direction of the force is the direction ofthe electric field.Wed. Feb 27, 2006 Phy107 Lecture 168The electric field++Force on this charge……due to this charge+++ ! Force = Charge( ) " Electric field( )! F = kQ1Q2r2Q1Q2Wed. Feb 27, 2006 Phy107 Lecture 169Question• Which vector best represents the force on a(positively charged) test particle at the reddot? (Think superposition!)A. AB. BC. CD. DE. E-ABC-DEWed. Feb 27, 2006 Phy107 Lecture 1610Visualizing the electric field• Faraday invented the idea of field linesfollowing the force tovisualize the electric field.Local electric field is samedirection as field lines.Force is parallel or antiparallelto field lines.Charged particle will movealong these field lines. Field lines emanate frompositive charge and terminateon negative charge.Wed. Feb 27, 2006 Phy107 Lecture 1611Why bother?• Why invent fields - why not just use forces?• Think of the EM wave. A spark is an acceleratingcurrent flow, producing the wave.• The wave continues to propagateeven when the spark is gone.• No charges anywhere,but time-varying fields propagate as a wave.Wed. Feb 27, 2006 Phy107 Lecture 1612Electric field: summary• Electric field ->will be a force on a charged particle.• This force ( and electric field) can arise fromelectric charges (via Coulomb’s law)• But once electric field is known, don’t needto know the charges that produce it.3Wed. Feb 27, 2006 Phy107 Lecture 1613Magnets• Clearly magnets interact with each other• Sometimes attracting, sometimes repelling• But the magnetic particles are sort of a ‘composite’positive and negative ‘magnetic charge’.• Visualized as a bar with positive pole (North) at oneend and negative pole (South) at other.• These ‘magnetic charges’ cannot be broken apart —always appear in N-S pairs.NSWed. Feb 27, 2006 Phy107 Lecture 1614Magnetism: Permanent magnets• North Pole and South Pole• This is the elementarymagnetic particle• Called magnetic dipole(North poleand South pole)• Poles interact with eachother similar to charges.NSNSNSSNLikes repelOppositesattractWed. Feb 27, 2006 Phy107 Lecture 1615Alignment force• But really one of the magnets is trying to align the other one.Which way will these magnets tend to align?NSNSNSNS NSNSNSSNA B C DWed. Feb 27, 2006 Phy107 Lecture 1616Magnetic field• Similar in spirit to electric field• Used to determine ‘orientational’force on a compass needle:– Magnetic field exerts a force oncompass needle– Aligns it with magnetic field lines.• Magnetic field lines indicatedirection of local magnetic field• Start at N pole, end at S poleNSWed. Feb 27, 2006 Phy107 Lecture 1617The Earth is a magnet!Earth is a barmagnet.North magneticpole ~ at southgeographic poleA compass is abar magnetCompass needle alignswith local Earth fieldWed. Feb 27, 2006 Phy107 Lecture 1618Surprise! Electric currentproduces magnetic field• Current (flow of electric charges )in wire produces magnetic field.• That magnetic field aligns compass needleCurrentMagneticfield4Wed. Feb 27, 2006 Phy107 Lecture 1619Magnetic field from a currentIron filings align withmagnetic field linesMagnetic field loopsaround the current.Wed. Feb 27, 2006 Phy107 Lecture 1620Magnetic force on electric charges• Effect of uniform B-field on charged particle– Charged particle not moving• no effect– Charged particle is moving:• force exerted perpendicularto both field andvelocityWed. Feb 27, 2006 Phy107 Lecture 1621Magnetic Force on a Current• Force on each moving charge• Charges trapped in wire• -> force on wire when currentis flowingSNICurrentMagnetic fieldMagnetic forceWed. Feb 27, 2006 Phy107 Lecture 1622‘Homopolar’ motorWhy does the motor turn?A. Electric Coulomb forcepushes on magnetB. Magnetic field pushes oncurrent from batteryC. Current from battery heatsthe magnetD. Current through wireproduces magnetic fieldWed. Feb 27, 2006 Phy107 Lecture 1623Forces between currents• Which of these pairs of currents will attracteach other?A. AB. A & CC. BA B CWed. Feb 27, 2006 Phy107 Lecture 1624Time-varying magnetic field• Up to this point,electric and magnetic fields constant in time• Constant electric currentproduces constant magnetic field.• Constant magnetic fieldproduces… nothing in particular!• But changing the magnetic field in timeproduces… an electric field!• This effect is called induction.5Wed. Feb 27, 2006 Phy107 Lecture 1625Faraday’s law of inductionFaraday’s law:– time-varying magnetic fieldproduces electric field– Strength of electric field proportionalto how fast magnetic field changes.In this experiment:• Magnetic field is largest close to thebar magnet, drops off farther away.• Moving magnet
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