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charged particles in magnetic field.pdf
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?=KH; !NMQGRGTCJWAF?PECBM@HCARKMTGLEBSCUCQRGL?PCEGMLUFCPCRFC%?PRFxQK?ELCRGADGCJBGQBSCLMPRFCVNCPGCLACQ?DMPACRF?RGQQRP?GEFRBMUL?QQFMUL! LCE?RGTCAF?PECKMTGLEGLRFCQ?KCBGPCARGMLUMSJBDCCJ?DMPACQRP?GEFRSN ,JH7J;=O 7C?PCEGTCLRFCAF?PECGRQTCJMAGRW?LBRFCK?ELCRGADGCJBQRPCLERF?LBBGPCARGML7CA?LRFSQSQCRFCCOS?RGML F = qvB sin θ RMDGLBRFC DMPAC ,EBKJ?ED 4FCK?ELCRGADMPACGQ F = qvb sin θ. 7CQCCRF?R sin θ = 1 QGLACRFC?LEJC@CRUCCLRFCTCJMAGRW?LBRFCBGPCARGMLMDRFCDGCJBGQ 90º %LRCPGLERFCMRFCPEGTCLOS?LRGRGCQWGCJBQ F = ⎛⎝20×10–9 C⎞⎠(10 m/s)⎛⎝5×10–5 T⎞⎠
?I9KII?ED 4FGQDMPACGQAMKNJCRCJWLCEJGEG@JCML?LWK?APMQAMNGAM@HCARAMLQGQRCLRUGRFCVNCPGCLAC)RGQA?JASJ?RCBRMMLJWMLCBGEGRQGLACRFC%?PRFxQDGCJB T?PGCQUGRFJMA?RGML?LBGQEGTCLRMMLJWMLCBGEGR 4FC%?PRFxQK?ELCRGADGCJBFMUCTCPBMCQNPMBSACTCPWGKNMPR?LRCDDCARQN?PRGASJ?PJWML QS@KGAPMQAMNGAN?PRGAJCQ3MKCMDRFCQC?PCCVNJMPCBGL EH9;ED7&EL?D=>7H=;?D7&7=D;J?9?;B:N7CFB;I7D:FFB?97J?EDI |
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UFGAF?NNPM?AFRFC%?PRF4FCWA?L@CDMPACBGLRMQNGP?JN?RFQ@WRFC%?PRFxQK?ELCRGADGCJB0PMRMLQGLEG?LR?AACJCP?RMPQ?PCICNRGL?AGPASJ?PN?RF
@WK?ELCRGADMPAC4FC@S@@JCAF?K@CPNFMRMEP?NFGL ?=KH; QFMUQAF?PECBN?PRGAJCQKMTGLEGLQSAFASPTCBN?RFQ4FCASPTCBN?RFQMD
AF?PECBN?PRGAJCQGLK?ELCRGADGCJBQ?PCRFC@?QGQMD?LSK@CPMDNFCLMKCL??LBA?LCTCL@CSQCB?L?JWRGA?JJWQSAF?QGL?K?QQQNCARPMKCRCP
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Fc = mv2/ r .MRGLERF?R sin θ = 1 UCQCCRF?R F = qvB
?=KH; !LCE?RGTCJWAF?PECBN?PRGAJCKMTCQGLRFCNJ?LCMDRFCN?ECGL?PCEGMLUFCPCRFCK?ELCRGADGCJBGQNCPNCLBGASJ?PGLRMRFCN?ECPCNPCQCLRCB@WRFCQK?JJAGPAJCQ UGRFVxQvJGICRFCR?GJQMD?PPMUQ 4FCK?ELCRGADMPACGQNCPNCLBGASJ?PRMRFCTCJMAGRW?LBQMTCJMAGRWAF?LECQGLBGPCARGML@SRLMRK?ELGRSBC5LGDMPKAGPASJ?PKMRGMLPCQSJRQ
"CA?SQCRFCK?ELCRGADMPAC F QSNNJGCQRFCACLRPGNCR?JDMPAC Fc UCF?TC
qvB = mvr2.
3MJTGLEDMP r WGCJBQ
r = mv. qB
(CPC r GQRFCP?BGSQMDASPT?RSPCMDRFCN?RFMD?AF?PECBN?PRGAJCUGRFK?QQ m ?LBAF?PEC q KMTGLE?R?QNCCB v NCPNCLBGASJ?PRM?K?ELCRGA
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!K?ELCR@PMSEFRLC?P?LMJB D?QFGMLCB46QAPCCLQSAF?QGL ?=KH; 46QCRQUGRFA?RFMBCP?WRS@CQGLQRC?BMD,#$QAPCCLQ QCTCPCJW BGQRMPRQGRQNGARSPC@W?JRCPGLERFCN?RFMDRFCCJCARPMLQRF?RK?ICGRQNFMQNFMPQEJMU 10>664:6+,5$6+1/($5,69,..2(4/$0(06.:/$*0(6,;( $0'47,06+( 4MGJJSQRP?RCRFGQA?JASJ?RCRFCP?BGSQMDASPT?RSPCMDRFCN?RFMD?LCJCARPMLF?TGLE?TCJMAGRWMD 6.00×107 m/s AMPPCQNMLBGLERMRFC?AACJCP?RGLETMJR?ECMD?@MSRI6SQCBGLQMKC46Q NCPNCLBGASJ?PRM?K?ELCRGADGCJBMDQRPCLERF B = 0.500 T M@R?GL?@JCUGRFNCPK?LCLRK?ELCRQ
?=KH; 3GBCTGCUQFMUGLEUF?RF?NNCLQUFCL?K?ELCRAMKCQGLAMLR?ARUGRF?AMKNSRCPKMLGRMPMP46QAPCCL%JCARPMLQKMTGLERMU?PBRFCQAPCCLQNGP?J?@MSR K?ELCRGADGCJBJGLCQK?GLR?GLGLERFCAMKNMLCLRMDRFCGPTCJMAGRWN?P?JJCJRMRFCDGCJBJGLCQ4FGQBGQRMPRQRFCGK?ECMLRFCQAPCCL ,JH7J;=O 7CA?LDGLBRFCP?BGSQMDASPT?RSPC r BGPCARJWDPMKRFCCOS?RGML r = mv QGLAC?JJMRFCPOS?LRGRGCQGLGR?PCEGTCLMPILMUL qB ,EBKJ?ED 5QGLEILMULT?JSCQDMPRFCK?QQ?LBAF?PECMD?LCJCARPML?JMLEUGRFRFCEGTCLT?JSCQMD v ?LB B EGTCQSQ ⎛⎝ −31 ⎞⎠⎛⎝ .00×107 m/s⎞⎠ mv = 9.11×10 kg 6 r = ⎝ = 6.83×10−4 m MP r = 0.683 mm. ?I9KII?ED 4FCQK?JJP?BGSQGLBGA?RCQ?J?PECCDDCAR4FCCJCARPMLQGLRFC46NGARSPCRS@C?PCK?BCRMKMTCGLTCPWRGEFRAGPAJCQEPC?RJW?JRCPGLERFCGPN?RFQ ?LBBGQRMPRGLERFCGK?EC |
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