4-Electricity Magnetism 12-13

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1、UVAPHYSICSDEPARTMENTPHDQUALIFYINGEXAMPROBLEMFILEELECTRICITYANDMAGNETISMUPDATED:DECEMBER4,20131.(a)Computetheelectricfieldandpotentialduetoaninfinitelylongstraightlineofchargeoflineardensity.(b)Nowconsidertwoparallelandoppositelychargedlinesoflinearchargedensitiesand−κseparatedbyvect

2、orgoingperpendicularlyfromthenegativelychargedlinetothepositivelychargedline.Thissystemthereforehasdipolemomentperunitlength.Computethepotentialoftheelectricfieldofsuchadipoleatalocationsatisfyingtheconditionr>>a,whereisatwo-dimensionalvectorinaplaneperpendiculartothelines,theorigin

3、beingatthemidpointofthetwolines.)2.Twoelectronsareseparatedbyadistancerinthex-direction.Assumingtheelectronspinsarebothpointinginthey-direction,determinetheratioofthemagneticinteractionforcebetweentheelectronstotheelectricforcebetweentheelectrons.Howdoesthemagneticforcechangeifoneof

4、thespinsisturnedtopointinthenegativey-direction?Comparethetotalmagneticpluselectrostaticinteractionenergyofthetwoelectronswithparallelspinstothatofelectronswithanti-parallelspins.3.Aphotonofenergyεcollideswithastationaryelectronofmassmandemergesafterthecollisionatanangleθwithrespect

5、tothedirectionofitsoriginalmotion.Computetheenergyofthephotonafterthecollision.Donotassumethattheelectronmotionisnon-relativistic.Whatisthenameoftheeffectdescribedinthisproblem?4.Achargedparticlewithavelocityvistravelinginamediumofpermittivityε.a)(1point)Atwhatthresholdvelocitywillt

6、heparticleemitČerenkovlight?b)(2)DeriveanexpressionfortheangleofemissionoftheČerenkovradiationintermsofthevelocityoftheparticle,andthepermittivity.Ifyouuseagraphicmethodshowyourdiagram(carefullylabeled).1ElectrictiyandMagnetismDecember2013c)(2)Considertwomedia,onewithnandasecondwith

7、nwherenn>.Inwhich1212mediumwillthethresholdvelocityforemissionofČerenkovradiationbelarger?WhichmediumwillhavethelargerČerenkovangleatagivenvelocity?d)(1)IsČerenkovradiationcoherentorincoherent?e)(1)WhatisthestateofpolarizationofČerenkovradiation?Argueforyouranswer.(Hint:rememberthee

8、lectricandmagneticf