GeneralPhysics(PHY2140)Lecture13ElectricityandMagnetismMagnetismApplicationofmagneticforcesAmpere’slawChapter19:///~apetrov/PHY2140/11/26/20231LightningReviewLastlecture:

MagnetismMagneticfieldMagneticforceonamovingparticleMagneticforceonacurrentReviewProblem:

Howdoestheauroraborealis(theNorthernLights)work?11/26/20232MagneticFieldoftheEarth11/26/20233ReviewProblem2Howdoesyourcreditcardwork?Thestripeonthebackofacreditcardisamagneticstripe,oftencalledamagstripe.Themagstripeismadeupoftinyiron-basedmagneticparticlesinaplastic-likefilm.Eachparticleisreallyatinybarmagnetabout20-millionthsofaninchlong.Themagstripecanbe"written"becausethetinybarmagnetscanbemagnetizedineitheranorthorsouthpoledirection.Themagstripeonthebackofthecardisverysimilartoapieceofcassettetape.Amagstripereader(youmayhaveseenonehookedtosomeone'sPCatabazaarorfair)canunderstandtheinformationonthethree-trackstripe.11/26/20234ReviewExample1:FlyingduckAduckflyinghorizontallyduenorthat15m/spassesoverAtlanta,wherethemagneticfieldoftheEarthis5.0×10-5Tinadirection60°belowahorizontallinerunningnorthandsouth.Theduckhasapositivechargeof4.0×10-8C.Whatisthemagneticforceactingontheduck?11/26/20235ReviewExample2:WireinEarth’sBFieldAwirecarriesacurrentof22Afromeasttowest.Assumethatatthislocationthemagneticfieldoftheearthishorizontalanddirectedfromsouthtonorth,andhasamagnitudeof0.50x10-4T.Findthemagneticforceona36-mlengthofwire.Whathappensifthedirectionofthecurrentisreversed?B=0.50x10-4T.I=22Al=36mFmax=BIl11/26/2023619.5TorqueonaCurrentLoopImagineacurrentloopinamagneticfieldasfollows:BIbaBa/2FFFF11/26/20237BIbaBa/2FFFF11/26/20238Inamotor,onehas“N〞loopsofcurrent11/26/20239Example1:TorqueonacircularloopinamagneticfieldAcircularloopofradius50.0cmisorientedatanangleof30.0otoamagneticfieldof0.50T.Thecurrentintheloopis2.0A.Findthemagnitudeofthetorque.B30.0or=0.500mq

=30oB=0.50TI=2.0AN=111/26/202310Example2:triangularloopA2.00mlongwirecarryingacurrentof2.00Aformsa1turnloopintheshapeofanequilateraltriangle.Iftheloopisplacedinaconstantmagneticfieldofmagnitude0.500T,determinethemaximumtorquethatactsonit.11/26/20231119.6Galvanometer/ApplicationsDeviceusedintheconstructionofammetersandvoltmeters.MagnetCurrentlooporcoilSpringScale11/26/202312GalvanometerusedasAmmeterTypicalgalvanometerhaveaninternalresistanceoftheorderof60W-thatcouldsignificantlydisturb(reduce)acurrentmeasurement.Builttohavefullscaleforsmallcurrent~1mAorless.Mustthereforebemountedinparallelwithasmallresistororshuntresistor.Galvanometer60WRp11/26/202313Galvanometer60WRpLet’sconverta60W,1mAfullscalegalvanometertoanammeterthatcanmeasureupto2Acurrent.Rpmustbeselectedsuchthatwhen2Apassesthroughtheammeter,only0.001Agoesthroughthegalvanometer.Rpisrathersmall!Theequivalentresistanceofthecircuitisalsosmall!11/26/202314GalvanometerusedasVoltmeterFiniteinternalresistanceofagalvanometermustalsoaddressedifonewishestouseitasvoltmeter.Mustmountedalargeresistorinseriestolimitthecurrentgoingthoughthevoltmeterto1mA.Mustalsohavealargeresistancetoavoiddisturbingcircuitwhenmeasuredinparallel.Galvanometer60WRs11/26/202315Galvanometer60WRsMaximumvoltageacrossgalvanometer:Supposeonewishtohaveavoltmeterthatcanmeasurevoltagedifferenceupto100V:Largeresistance11/26/20231619.7MotionofChargedParticleinmagneticfieldConsiderpositivelychargeparticlemovinginauniformmagneticfield.Supposetheinitialvelocityoftheparticleisperpendiculartothedirectionofthefield.Thenamagneticforcewillbeexertedontheparticleandmakefollowacircularpath.′′

′′′′′′′′′′′′′′′′′′′′′′′′′′FvqrBin11/26/202317Themagneticforceproducesacentripetalacceleration.Theparticletravelsonacirculartrajectorywitharadius:11/26/202318Example1:ProtonmovinginuniformmagneticfieldAprotonismovinginacircularorbitofradius14cminauniformmagneticfieldofmagnitude0.35T,directedperpendiculartothevelocityoftheproton.Findtheorbitalspeedoftheproton.r=0.14mB=0.35Tm=1.67x10-27kgq=1.6x10-19C11/26/202319Example2:Considerthemassspectrometer.Theelectricfieldbetweentheplatesofthevelocityselectoris950V/m,andthemagneticfieldsinboththevelocityselectorandthedeflectionchamberhavemagnitudesof0.930T.Calculatetheradiusofthepathinthesystemforasinglychargedionwithmassm=2.18×10-26kg.11/26/20232019.8MagneticFieldofalongstraightwireDanishscientistHansOersted(1777-1851)discoveredsomewhatbyaccidentthatanelectriccurrentinawiredeflectsanearbycompassneedle.In1820,heperformedasimpleexperimentwithmanycompassesthatclearlyshowedthepresenceofamagneticfieldaroundawirecarryingacurrent.I=0I11/26/202321MagneticFieldduetoCurrentsThepassageofasteadycurrentinawireproducesamagneticfieldaroundthewire.FieldformconcentriclinesaroundthewireDirectio