Electrical Mobility equation (Einstein's relation)

The Electrical Mobility Diffusion calculator computes the constant based on electrical mobility of the charged particle, the Boltzmann constant, the electron temperature and the electrical charge of a particle.

INSTRUCTIONS: Choose units and enter the following:

• (μ_q)  This is the electrical mobility of the charged particle in units m²/(V⋅s)
• (T)  This is the electron temperature
• (q)  This is the electrical charge of a particle

Diffusion Constant (D): The calculator return the diffusion in stokes (cm²/s).

The Math / Science

The Electrical Mobility equation  is a form of Einstein's relation. For a particle with electrical charge q, its electrical mobility μ_q is related to its generalized mobility `mu` by the equation μ =μ_q/q. The parameter μ_q is the ratio of the particle's terminal drift velocity to an applied electric field. Hence, the formula for the Electrical Mobility of a charged particle is:

        D = (μ_q • k_B • T)/q

where:

• D = diffusion
• μ_q = electrical mobility of the charged particle
• k_B = Boltzmann Constant
• T = electron temperature
• q = electrical charge of a particle

References

Wikipedia (https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory))