Electromagnetism exercise

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1、1.1AmagneticcircuitwithasingleairgapisshowninFig.1.24.Thecoredimensionsare:Cross-sectionalareaMeancorelengthGaplengthturnsAssumethatthecoreisofinfinitepermeability()andneglecttheeffectsoffringingfieldsattheairgapandleakageflux.(a)Calculatethereluctanceofthecoreandthatofthegap.Foracurrentof,calculat

2、e(b)thetotalflux,(c)thefluxlinkagesofthecoil,and(d)thecoilinductanceL.Sol:已知(a)(b)(c)(d)1.1RepeatProblem1.1forafinitecorepermeabilityof.Sol(a):(b)(c)(d)1.3ConsiderthemagneticcircuitofFig.1.24withthedimensionsofProblem1.1.Assuminginfinitecorepermeability,calculate(a)thenumberofturnsrequiredtoachieve

3、aninductanceof12mHand(b)theinductorcurrentwhichwillresultinacorefluxdensityof1.0T.Figure1.24Sol:part(a):因為又而又所以可以得到part(b):因為習題1.1忽略了邊緣效應所以又又所以因此可以得到1.6ThemagneticcircuitofFig.1.25consistsofacoreandamoveableplungerofwidthlp,eachofpermeabilityμ.Thecorehascross-sectionalareaAc,andmeanlengthlc,Theover

4、lapareaofthetwoairgapsAgisafunctionoftheplungerpositionxandcanbeassumedtovaryasYoumayneglectanyfringingfieldsattheairgapanduseapproximationsconsistentwithmagnetic-circuitanalysis.a.Assumingthatμ→∞,deriveanexpressionforthemagneticfluxdensityintheairgapBgasafunctionofthewindingcurrentIandastheplunger

5、positionisvaried(0≤x≤0.8X0).Whatisthecorrespondingfluxdensityinthecore?b.Repeatpart(a)forafinitepermeabilityμ.Figure1.25MagneticcircuitforProblem1.6.Sol:part(a):因為又所以因為所以part(b):因為又所以最後得到1.8Fig1.24AninductoroftheformofFig1.24hasdimensions:Cross-sectionalareaAc=3.6Meancorelengthlc=15cmN=75turnsAssum

6、ingacorepermeabilityofandneglectingtheeffectsofleakagefluxandfringingfields，calculatetheair-gaplengthrequiredtoachieveaninductanceof6.0mHSol：1.9Fig1.26Themagneticcircuitoffig1.26consistsofmagneticmaterialinastackofheighth.TheingshaveinnerradiusRiandouterradiusRo.Assumethattheironisofinfiniteermeabi

7、lity（）andneglecttheeffectsofmagneticandfringing.ForRi=3.4cmRo=4.0cmh=2cmg=0.2cmcalculate（a）Themeancorelengthlcandthecorecross-sectionalareaAc（b）ThereluctanceofthecoreRcandthatofthegapRg（N=65）（c）Theinductanc