Question

Write the mathematical relation between mobility and drift velocity of charge carriers in a conductor. Name the mobile charge carriers responsible for conduction of electric current in 1) an electrolyte 2) an ionised gas.

Answer 1

Hint: In this question we have been asked to state the mathematical relation between the mobility and drift velocity of the charge carriers in conductor. We have also been asked to state the charge carriers in an electrolyte and ionised gas. Therefore, to answer this question we shall discuss what is mobility and drift velocity. We shall write the formula to calculate the same. While doing so, we shall establish a relation between mobility and drift velocity.

Complete answer:
We know that the average velocity attained by the charged particles in a conductor due to an electric field is known as the drift velocity. When a potential difference is applied across the conductor, free electrons gain velocity in the opposite direction of the electric field. As a result, there is small drift velocity.
 The equation to calculate drift velocity can be given by,
\[{{v}_{d}}=\dfrac{I}{neA}\]
Where
I is the current
e is the charge on electron
A is the area
n is the free electron density.
Mobility is defined as the value of drift velocity over electric field strength. Therefore, higher the drift velocity of the particle higher is the mobility. Which means that the electron will travel at higher speed.
The equation of mobility is given as
\[\mu =\dfrac{{{v}_{d}}}{E}\]
Where
\[\mu \] is the mobility
E is the electric field.
In an electrolyte the charge carriers are both positive and negative ions.
In an ionised gas the charge carriers are electrons and positive ions.

Note:
Mobility of a charge carrier is the average velocity with which the carrier moves towards the positive end of the conductor under the applied potential difference. The mobility of electrons as a charge carrier is greater than holes. Mobility can also be defined as the ability to move freely. In general, the electron in a conductor will move with a fermi velocity, resulting in zero average velocity. Applying voltage adds to this net velocity and a drift is observed.