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Derive the expression for conductivity in terms of mobility

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11,325 views asked Jan 3, 2018 in Electricity & Magnetism by sarojgope (150 points)

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The electron mobility is defined by the equation:

\,v_{d}=\mu E.


E is the magnitude of the electric field applied to a material,
vd is the magnitude of the electron drift velocity (in other words, the electron drift speed) caused by the electric field, and
µ is the electron mobility.

There is a simple relation between mobility and electrical conductivity. Let n be the number density (concentration) of electrons, and let μe be their mobility. In the electric field E, each of these electrons will move with the velocity vector -\mu _{e}\mathbf {E}, for a total current density of ne\mu _{e}\mathbf {E} (where e is the elementary charge). Therefore, the electrical conductivity σ satisfies:

\sigma =ne\mu _{e}.

This formula is valid when the conductivity is due entirely to electrons



answered Jan 5, 2018 by admin (4,920 points)

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