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Stokes force
Equation 
The resistance is defined in terms of the fluid viscosity and the sphere's velocity as follows:
| $ F_v = b v $ |
Stokes explicitly calculated the resistance experienced by the sphere and determined that viscosity is proportional to the sphere's radius and its velocity, leading to the following equation for resistance:
 $ F_v =6 \pi \eta r v $ |
ID:(4871, 0)
Particle velocity in electric field
Equation
A charged particle
| $ F = q E $ |
This force is opposed by a force due to the effect of the medium that can be modeled by Stokes law
| $ F_v =6 \pi \eta r v $ |
If both forces are equalized, it is obtained that the particle moves with a constant speed equal to
| $ \vec{v} = \mu \vec{E} $ |
with mobility equal to
| $ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$ |
ID:(11997, 0)
Particle mobility in electric field
Equation
To equalize the force caused by the electric field
| $ F = q E $ |
with the opposing force that is modeled with Stokes law
| $ F_v =6 \pi \eta r v $ |
the relationship is obtained
| $ \vec{v} = \mu \vec{E} $ |
with mobility equal to
| $ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$ |
ID:(11998, 0)