Lecture_22_(Chap.23)

# Lecture_22_(Chap.23) - Maxwells Equations(incomplete E ndA...

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Maxwell’s Equations (incomplete) ˆ inside q dA n E Gauss’s law for electricity 0 ˆ 0 B ndA  Gauss’s law for magnetism 0 l d E Incomplete version of Faraday’s law mpere’slaw path inside I l d B _ 0 Ampere s law (Incomplete Ampere-Maxwell law) First two: integrals over a surface Second two: integrals along a path Incomplete: no time dependence 1

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Electric and Magnetic Fields Electric and magnetic fields are interconnected Moving charges make magnetic fields Magnetic fields affect moving charges lectric and magnetic fields depend on reference frame Electric and magnetic fields depend on reference frame Change reference frame: magnetic field is converted into electric and vise versa. Today we’re looking at time varying magnetic field: It can produce electric field! (magnetic induction) 2

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Currents Due to Magnetic Forces Metal bar B v q E q F e v B    m Fe  polarization F Static equilibrium: 0 F m B v e E e ) ( ) ( vB E Metal is in static equilibrium: but E 0 inside! What is V ? vBL EL V How about moving B (or changing B)? 4
Non-Coulomb Work on oulomb force Non-Coulomb force drives e against F E F m Non-Coulomb work: evBL L F NC What is emf of this ‘battery’? Non-Coulomb work per unit charge: vBL e L F NC vBL emf V ‘motional emf’ Bar may have some resistance r int : I r emf V int 5

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Changing Magnetic Field Solenoid: inside d NI B 0 outside 0 B Constant current: there will be no forces on charges outside (B=0, E=0) What if current is not constant in time? Let B increase in time 1 / r ~dB/dt E~1/r EdB / d t Non-Coulomb E NC !
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Lecture_22_(Chap.23) - Maxwells Equations(incomplete E ndA...

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