Mobility of Charged Particle

       Consider a material having a large number of free electrons. It is electrically neutral i.e. number of protons. All the free electrons move around randomly inside the material. As the motion is random, on an average, the number of electrons passing through unit area in a given time in any direction inside the material is same as the number of electrons passing in opposite direction. Hence net movement of the electrons is cancelled. And hence without electric field, there can not by any drift current in the material.
       Consider a material of length L, subjected to the voltage V as shown in the Fig 1. The electric field to which it is subjected is given by,
                        E = V/L      V/m                                     ................. (1)
       The free electrons drift inside the material constituting the drift current.
       Finally a steady state condition is reached when electrons continue to move with a finite steady velocity. Such a speed attained by the electrons under the influence of applied electric field in steady state condition is called as drift speed or drift velocity. It is denoted by v measured in meters per second. The magnitude of the drift velocity is proportional to the electric field E, so mathematically we can write
                                    v α E
...                                 v = μ E                                                    .................(2)
      where                     v = Drift velocity in m/sec
                                    E = Applied electric field in v/m
       Where μ is constant of proportionality and is called mobility of the electrons. This is applicable to the free electrons as well as the holes whichever are the majority carriers.
       So in general ,
       μ = Mobility of a charged particle = v/E

       So it is measured in square meters per volt-second. Such steady state movement of majority charge carriers with drift velocity constitutes a current. This current is called drift current.
Example : A bar of intrinsic germanium 6 cm long is subjected to a potential difference of 12 V. If the velocity of electrons in bar is 73 m/s, determine the mobility of electrons.
Solution : The given values are, 
       l = 6 cm = 6 x 10-2 m, V = 12 V, v = 73 m/sec
...       E = Electric field intensity = V/l = 12/(6 x 10-2) = 200 V/m
Now   v = μ E
...        73 = μ x 200
...         μ = Mobility = 73/200 = 0.3650 m2/V-sec = 3650 cm2/V-sec

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