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Thermodynamics in static electric and magnetic fields

Thermodynamics in static electric and magnetic fields. A. dielectric material. L. -q. -. V e. +. +q. 1 st law reads:. originates from mechanical work. -so far focus on PVT-systems where. Now:. -additional work terms for matter in fields. Source of D is density of. free charges.

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Thermodynamics in static electric and magnetic fields

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

  2. -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 parameterized e.g., with time(slow changes!) -Work done by the material exclusively:

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

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

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

  6. -Reduction of the current I work 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 M=0 No material rate at which work is done by the magnetic material

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

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