Thermodynamics in static electric and magnetic fields 1

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Thermodynamics in static electric and magnetic fields 1 st law reads: -so far focus

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 Source of D is density of 1 Dielectric Materials A + Ve -q free charges. Here: charge q on capacitor plate with area A L dielectric material +q -electric field inside the capacitor: -displacement field D given by the free charges on the capacitor plates:

-Reduction of q Energy content in capacitor reduced which means work Wcap>0 done by

-Reduction of q Energy content in capacitor reduced which means work Wcap>0 done by the capacitor (in accordance with our sign convention for PVT systems) (dq<0 and Ve>0 yields Wcap>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!)

With Polarization=total dipole moment per volume With (where V=const. is assumed so With that

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

-Legendre transformations (providing potentials depending on useful natural variables) making electric field E variable

-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

2 Magnetic Materials R I N: # of turns of the wire A: cross

2 Magnetic Materials R I N: # of turns of the wire A: cross sectional area of the ring where Faraday’s law: here voltage Vind induced in 1 winding Ampere’s law: where magn. flux lines

-Reduction of the current I work done by the ring per time makes sure

-Reduction of the current I 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: No material M=0 where M is the magnetization = magnetic dipole moment per volume rate at which work is done by the magnetic material

-Legendre transformations (providing potentials depending on useful natural variables) making magnetic field H variable

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