Summary so far:1.3 Completion of Maxwell equations:leads to contradictions for continuity equation Resolution:Change equations as followsNote: since replaceorandbyLec 03 - 9. JanThursday, January 08, 20099:51 AMLecture Notes Page 1
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Maxwell Equations:Note:Continuity Equation is now a consequence of Maxwell Equations1.4 Maxwell Equations & time evolution1.4.1: Problem structure for givensource distributionsconstraints:for given source distributionsatisfying the continuity equationtime evolution equations:Note:apparent asymmetry: -electric charge as source of E-field-but no basic source of B-field==> Maxwell theory could be extended by including magnetic monopoles magnetic currentsNo experimental evidence of magnetic monopoles and associated currents so far!Existence of magnetic monopoles would motivate quantization of electric charge==> see e.g. Jackson