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13. Comments about the induced electric field (nonelectrostatic field) 0 = l d E For electrostatic field: For induced (nonelectrostatic) field: 0 = ε l d E Electrostatic field is conservative Induced field is nonconservative When a charge goes around a closed loop work is equal to zero When a charge goes around a closed loop work is equal to: 0 = ε q W 0 = W Electric field lines do not form closed loops Electric field lines form closed loops

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Example: ? ? ? 90 10 0 . 1 2 1 2 1 - - - = = = V V I R R V ε 1 R 2 R 2 V 1 V ε 2 R 2 V 1 V 1 R A dt dB = ε a) battery b) Solenoid with changing field
Two questions: (1) How to find the force, F on the electric charge, q excreted by the field E and/or B? (2) How fields E and/or B can be created? B v q E q F × + = 2 r Q k E = Gauss’s law for electric field Electric charges create electric field: For one not moving (v<<c) charge: Gauss’s law for magnetic field Magnetic charges do not exist: Amperes law Electric current creates magnetic field:

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