Current Electricity
2.0 Conduction of current in a metal
2.0 Conduction of current in a metal
Metals have a large number of free electrons nearly ${10^{28}}$ per cubic meter.
In absence of electric field, these electrons are in a state of continuous random motion due to thermal energy.
Thermal Velocity
At room temperature, free electrons move randomly with velocities of order ${10^5}m{s^{ - 1}}$. This velocity is called thermal velocity.
However, an average thermal velocity of free electrons in any direction remains zero.
If ${\vec u_1},{\vec u_2}......{\vec u_n}$ are the random velocity of $N$ free electrons, then average velocity of electrons,$$\frac{{{{\vec u}_1} + {{\vec u}_2} + ......{{\vec u}_n}}}{N} = 0$$
Therefore, the conductor has no net flow of charge in any direction.
In presence of an electric field ($\vec E$), free electrons experiences force $(-e\vec E)$ in a direction opposite to that of the electric field $\vec E$.
Due to this force, electrons accelerate and collides with the ions or atoms of the metal. Between two successive collision, an electron gains a velocity component in the direction opposite to $\vec E$.
However, the gain in velocity lasts for short time and is lost in next collisions. At each collision, the electron starts a fresh motion in a random direction with random thermal velocity.
In the figure, solid lines represent path in absence of electric field and dashed lines represents a path in presence of electric field.
${\overrightarrow F _e}$ is the force on an electron due to the electric field $\left( {\overrightarrow E } \right)$
Mean free path
Mean free path is defined as the average distance traveled by an electron between two consecutive collisions.
Relaxation time
Relaxation time is defined as the time taken to travel mean free path is called relaxation time. It is denoted by Greek letter Tau,$\tau $
Drift Velocity
Drift velocity is defined as the average velocity gained by free electrons of a conductor in a direction opposite to that of $\vec E$.
