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7.11MagneticfluxdensityAroundanymagnetisedobjectthereisaregionofspacewherewecandetectamagneticfield.Wecandothisbyplacingacompassatanypointandnotingwhatdirectionitpoints.Thecompassconsistsofasmall,magnetisedbarwhichcontainsanorthandsouthpole.Themagneticfieldexertsatorque(turningforce)onthecompasscausingittoalignalongamagneticfieldline.

Inthisdiagram,left,youcanseethataplottingcompassispointingalongthedirectionofthemagneticfieldline.Magneticfieldlinesgofromanorth(N)magneticpoletoasouth(S)magneticpole.Magneticfieldlinesareknownaslinesofmagneticflux.

(1)!Wherewouldthemagneticfluxbethemostconcentrated?Howcanyoutellfromthediagram?Whenwepassanelectriccurrentthroughaconductingwireamagneticfieldisproducedinthespacearoundthewire.Themagneticfluxlineswraparoundthewireinacircle.Youcandeterminethedirectiontheypointbyusingtherighthandthumbrule.Thethumbpointsinthedirectionthatthecurrent(𝐼)flows,andthefingerswraparoundinthedirectionofthelinesofmagneticflux.Ifwewrapthewireintoacoil(calledasolenoid)wecanproduceamagneticfieldsimilartothatofabarmagnet.

Inthediagram,above,thedotsshowcurrentflowingupwards(outofthepage)andthecrossesshowcurrentflowingdownwards.

𝐼

𝐼

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(2)!Howwouldyoudescribethemagneticfielddownthemiddleofthesolenoid?Thestrengthofthemagneticfieldisknownasthemagneticfluxdensity(𝐵).(3)!Howcouldyouincreasethemagneticfluxdensityinthemiddleofthesolenoid?ThemotoreffectWhenacurrent-carryingwireisplacedinamagneticfielditexperiencesaforce.Thisisknownasthe‘motoreffect’.ThedirectionoftheforceonthewirecanbedeterminedusingFlemming’slefthandrule.

Ifyoupointyourfirstfingeralongthefielddirection(NtoS)andyoursecondfingerinthedirectionthatthecurrentisflowinginthewire,yourthumbwillshowthedirectionoftheforceonthewire.Thisforcearisesfromtheinteractionofthemagneticfieldandthemagneticfieldproducedbythecurrentflowinginthewire.

Thestrengthofthemagneticfield(magneticfluxdensity𝐵)canbedeterminedfromtheforceproduced.Theforce𝐹onalength𝑙ofwirecarryingacurrent𝐼isgivenby:

𝐹 = 𝐵𝐼𝑙(4)!Rearrangethisequationtomakethemagneticfluxdensity(B)thesubject.(5)!Fromthisequation,whataretheunitsformagneticfluxdensity?Themagneticfluxdensityisgivenitsownunitcalledthetesla(T).

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(6)!A3cmlengthofwirecarryingacurrentof2Aisplacedatrightanglestoauniformmagneticfield.Itexperiencesaforceof0.3N.Whatisthemagneticfluxdensity?(7)!UsingFlemming’sLeftHandRule,whatdirectionwouldtheforceactinthediagramabove?Ifthecurrent-carryingwireisnotatrightanglestothemagneticfluxlines,thentheforcewillbeless.Theforceonthewireisthereforemodified:

𝐹 = 𝐵𝐼𝑙 sin 𝜃where𝜃istheanglebetweenthecurrentdirectionandthemagneticfluxlines.(8)!Whatwouldtheforcebeiftheangle𝜃iszero?

I B

I B𝜃

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