1Mon. Feb 20, 2006 Phy107 Lecture 141From Last Time…• Electromagnetic waves• Charges, current and forces: Coulomb’s law.• Accelerating charges producean electromagnetic wave• The idea of the electric field.Today…Electric fields, magnetic fields, and theirunificationMon. Feb 20, 2006 Phy107 Lecture 142Eventually transatlantic signals!Gulgielmo Marconi’s transatlantic transmitterCapacitorbanksInductioncoilsSpark gapMon. Feb 20, 2006 Phy107 Lecture 143Electromagnetic Wavesxzy• A Transverse wave.• Electric and magnetic fields are perpendicular topropagation direction• Can travel in empty spacef = v/λv = c = 3 x 108 m/s (186,000 miles/second!)Mon. Feb 20, 2006 Phy107 Lecture 144The 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.Mon. Feb 20, 2006 Phy107 Lecture 145Question• Direction of force between two particles ofthe same charge (use next slide).Mon. Feb 20, 2006 Phy107 Lecture 146The electric field++Force on this charge……due to this charge+++ ! Force = Charge( ) " Electric field( )! F = kQ1Q2r2Q1Q22Mon. Feb 20, 2006 Phy107 Lecture 147Visualizing 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.Mon. Feb 20, 2006 Phy107 Lecture 148Why 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.Mon. Feb 20, 2006 Phy107 Lecture 149Electric field: summary• Presence of electric field means that therewill be a force on a charged particle.• This force ( and electric field) can arise fromelectric charges (via Coulomb’s law)• Is a way to determine forces on a chargedparticle without thinking about the chargesthat give rise to the forces.Mon. Feb 20, 2006 Phy107 Lecture 1410But wait… there’s more• Energy can be stored in the field.• Energy density proportional to(Electric field)2(Magnetic field)2• Electromagnetic forces aren’t feltinstantaneously, the propagate at speed ofelectromagnetic wave (speed of light)• Object transfers momentum to the field, whichlater transfers it to another object.Mon. Feb 20, 2006 Phy107 Lecture 1411Magnetic forces• 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.NSMon. Feb 20, 2006 Phy107 Lecture 1412Magnetism: 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 repelOppositesattract3Mon. Feb 20, 2006 Phy107 Lecture 1413Magnetic field• Similar in spirit to electric field• Used to determine the ‘orientational’ force on amagnetic dipole:– Magnetic field exerts a force on a dipole that aligns itwith magnetic field lines.– Uniform magnetic field only rotates dipole: doesn’t causeit to move.• Static magnetic fieldarises from permanent magnets (or currents).• But, as electric field, can exist in an EM waveeven without magnetic dipoles.Mon. Feb 20, 2006 Phy107 Lecture 1414Field lines of a magnet• Field lines indicatedirection of field• Density indicatesstrength of field• Similar toelectrostatic force,but force is felt bymagnetic dipoleMon. Feb 20, 2006 Phy107 Lecture 1415The Earth is a magnet!Earth is amagnetic dipole.North magneticpole ~ at southgeographic poleA compass is amagnetic dipoleCompass needle alignswith local Earth fieldMon. Feb 20, 2006 Phy107 Lecture 1416Surprise! Electric currentproduces magnetic field• Current (flow of electric charges )in wire produces magnetic field.• That magnetic field aligns compass needleCurrentMagneticfieldMon. Feb 20, 2006 Phy107 Lecture 1417Magnetic field from a currentIron filings align withmagnetic field linesMagnetic field loopsaround the current.Mon. Feb 20, 2006 Phy107 Lecture 1418Forces between currents• Which of these pairs of currents will attracteach other?A. AB. A & CC. BA B C4Mon. Feb 20, 2006 Phy107 Lecture 1419Magnetic field from a current loop• One loop:field still loops around the wire.• Many loops: same effectMon. Feb 20, 2006 Phy107 Lecture 1420Solenoid electromagnet• Sequence of currentloops can producestrong magneticfields.• This is anelectromagnetMon. Feb 20, 2006 Phy107 Lecture 1421Superconducting Magnets• Solenoid as inconventionalelectromagnet.• But once current isinjected, powersupply turned off,current and magneticfield stays forever……as long as T < TcMon. Feb 20, 2006 Phy107 Lecture 1422Magnetic Field RangesField Size ExampleField Size Example850 T60 T33 T2 T0.5 T0.4 T0.2 T0.01 T0.0001 T0.00003 T3x10-10 TMon. Feb 20, 2006 Phy107 Lecture 1423Magnets for MRI• Magnetic ResonanceImaging typicallydone at 1.5 T• Superconductingmagnet to providesstatic magnetic field• Spatial resolution ofpositions of traceratomic nuclei.Mon. Feb 20, 2006 Phy107 Lecture 1424Large scale applicationsProposed ITERfusion test reactorSuperconductingmagnetPlasma confinementtorus5Mon. Feb 20, 2006 Phy107 Lecture 1425Time-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.Mon. Feb 20, 2006 Phy107 Lecture 1426Faraday’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
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