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Thermodynamics in static electric and magnetic fields 1 st law reads: -so far focus on PVT-systems where originates from mechanical work Now: -additional work terms for matter in fields Dielectric Materials 1 1 -electric field inside the capacitor: A + - VeVe dielectric material L +q -q -displacement field D given by the free charges on the capacitor plates: Source of D is density of free charges. Here: charge q on capacitor plate with area A

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-Reduction of qEnergy content in capacitor reduced which means work W cap >0 done by the capacitor ( in accordance with our sign convention for PVT systems ) (dq 0 yields W cap >0) With V= volume of the dielectric material -When no material is present: still work is done by changing the field energy in the capacitor -Work done by the material exclusively: parameterized e.g., with time (slow changes!)

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With Polarization=total dipole moment per volume With ( where V=const. is assumed so that PdV has not to be considered ) Comparing ( where work is done mechanically via volume change against P ) With we define the total dipole moment of the dielectric material with Correspondenceand

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-Legendre transformations ( providing potentials depending on useful natural variables ) making electric field E variable H=H(S,E) making T variable G=G(T,E) and

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Magnetic Materials 2 2 I N: # of turns of the wire R Faradays law: where Amperes law: where here A: cross sectional area of the ring magn. flux lines voltage V ind induced in 1 winding

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-Reduction of the current Iwork done by the ring work done by the ring per time makes sure that reduction of B ( ) corresponds to work done by the ring -Again, when no material is present: still work is done on the source by changing the field energy In general: where M is the magnetization = magnetic dipole moment per volume No material M=0 rate at which work is done by the magnetic material

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-Legendre transformations ( providing potentials depending on useful natural variables ) making magnetic field H variable H enth =H enth (S,H) making T variable G=G(T,H) and

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