Using the distribution function of the previous problem, evaluate the electric current density J to show that

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Using the distribution function of the previous problem, evaluate the electric current density J to show that the presence of a temperature gradient gives rise to an electric current associated with thermoelectric effects.


Data from problem 10

An electron gas (Lorentz gas), in a background of stationary ions, is acted upon by a weak, externally applied electric field E, under steady state conditions. Using the Boltzmann equation for the electrons, with the relaxation model for the collision term (considering a constant collision frequency ν),

and considering the adiabatic case for which

show that the electron distribution function is given by

Assume that f = f0 + f1, where |f1| ≪ f0 and where f0 is the following modified Maxwellian distribution

and neglect all second-order terms in the Boltzmann equation. Consider the term involving ∇f1 as a second-order quantity.

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