Slide 1Slide 2Slide 3Slide 4Slide 52oiBrmp=The magnetic field due to a wire in 3DThe magnetic field due to a wire in 3DLike Coulomb’s Law:(For an infinite line charge)2oErlpe=Let’s think back to electrostaticsLet’s think back to electrostaticsencEo oqdre e� �F = � = �� =� �� ��E A Err r�•This is Gauss’ law, i.e. the more fundamental Maxwell This is Gauss’ law, i.e. the more fundamental Maxwell equation.equation.•It tells us that E-fields begin and end on electric charges.It tells us that E-fields begin and end on electric charges.•Provides a simple method for calculating E for certain Provides a simple method for calculating E for certain symmetries.symmetries.As far as we know, there is no magnetic equivalent of charge.As far as we know, there is no magnetic equivalent of charge.Therefore, magnetic field lines never begin or end.Therefore, magnetic field lines never begin or end.0 0Bd� �� F = � = �� =� ��B A Brr r�Consequently, Gauss’ law of no use in Consequently, Gauss’ law of no use in magnetostatics, since there is nothing with which to magnetostatics, since there is nothing with which to equate the flux of equate the flux of BB..By the way.....By the way......... we just derived (wrote down) the 2nd Maxwell .... we just derived (wrote down) the 2nd Maxwell equation!equation!Recall: electrostatic forces are Recall: electrostatic forces are conservativeconservative( ) ( ) b b ba a ad q d q V d q V a V b� = � =- � � = -� �� �� � �F s E s sr rr r r•This allowed us to define a scalar potential This allowed us to define a scalar potential VV..•Also implies..Also implies..0d� =�E srr�•Consequently, this integral is not much use in electrostatics.Consequently, this integral is not much use in electrostatics.•It is very important in electrodynamics (Maxwell’s 4th It is very important in electrodynamics (Maxwell’s 4th equation).equation).•However, this is because its However, this is because its not equal to zeronot equal to zero in in electrodynamics.electrodynamics.Maxwell’s 3rd equation (a.k.a. Maxwell’s 3rd equation (a.k.a. Ampère’s Law)Ampère’s Law)( )1 2o enc od i i im m� = = -�B srr�cos ;d Bds q� =� �B srr� �enc jSi d= � = F�j ArrRight-Right-hand-hand-ruleruleThe Magnetic Field of a DipoleThe Magnetic Field of a Dipole2, and iA A Rm p� �= =� �( )2 20 0 03/ 23 32 22 22iR i RBz zR zm m p m mp p= =+;ElectricdipoleMagneticdipoleBarmagnet3012pEzpe=(P. 26-1)At large distances (At large distances (zz >> >> RR) along the ) along the
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