南京大学大学物理答案15-16

Equilibriumrequiresthatallforcesarecancelled.04on2222xdqdqqFProblem15.104on2222xdqxqqF0444on2222dqxqqFAssumeoneofthesecharges,sayq,movesasmallDDDD~)()(42222xdqdqFqnotrestoringforce.Unstable.94;32dxEarshaw’sTheorem:Achargeparticlecannotbeheldinastableequilibriumbyelectrostaticforcesalone.Problem15.3Directlyusetheresultofdipole33212142ararpEPProblem15.3arapˆ243342425rqaraaqq–2qrPNBapqDefinejiRsincosRE2020d41RRProblem15.6R220d41RRi20441RQProblem15.9Aninfinitesheetofdx'atx'contributesafieldxxeaEd2410Outsidethesheet,E=02020)d(241)d(241)(mmxxxxxxeaxxeaxE2222024422xxxxeamm22022xxeamlefttox44141020rQESothefieldduetootherpartthandAisE212410outward.ThecontributionfromdA(veryclosetothesurface)is2410atbothsides.Totalfieldis*Problem15.12dAtotalTheforceondqisthenqEFd21dOtherpart?Problem15.15LPyxxV021220d41(a)yyLk2204(c)In(a)VP(0,y).ForExweneedV(x,y)LyyxxyE023220d4122014ddyLykyVEy(b)Problem16.1inseriesbdACC0121dAC0before2)(021bdACCafterbdAcopperqdaProblem16.3axdxaC00tandqaxxdda00d1qdada2120qaxdxda001dqProblem16.6xAqAqEe0r0d00dexAqVxdAVqe10xdVEee1KnownVProblem16.6Gauss’lawreads02EThepotentialdifferenceisRRERVRVRRln2d)()(0ThecapacityinunitlengthisRRCln20Problem16.402EAtinybumponoutsidewallisequivalentalittlelargerR',soCwillbesmalleralittlebit.901094dAC(a)Problem16.9Inthecaseq=const.doubleseparationmeanshalfthecapacitanceanddoubleenergy.Problem16.9142112100.22100.22CqU,100.214C100.211qJ100.1820212022121)1000(21VCVCCDD(b)V2000DVF108.8F100.1410100122400dAC(a)C108.8C100108.810120DVCq(b)cm,0.1,cm1002dAProblem16.4Adielectricslabofthicknessbanddielectricconstantisplacedbetweentheplatesofaparallel-platecapacitor.KnownProblem16.100.50cm=bV,100,0.70rV57V=cm50.0+cm50.0dgapDEEV(d)DEEuud2gap0dgap21:2:(e)or87.5%and12.5%(c)InthegapmV100.14000gapDdCVCAqE2gap02gap012:2EEr71:1