It is well-known fact that the conduction of electric current in a metallic conductor is due to free electrons. Every metal has a very large number of free electrons that randomly move within the body of the conductor. At room temperature, the average speed of these free electrons is very high, of the order of 10^5 m/s.
When the free electrons move randomly, they collide with the positive atoms of the metal conductor repeatedly. After each collision, the direction of motion of the free electrons changes. If we consider all the free electrons at a time, then there is no net flow of electrons in any particular direction because the average speed of all the free electrons is zero. As a result, there is no current through the conductor.
Now, if we applied a voltage across the ends of the metallic conductor (refer to the figure). An electric field is applied at every point of the conductor. This electric field forces the free electrons to move toward the positive terminal of the source. While moving towards the positive terminal, these electrons collide again and again with the positive atoms of the conductor. On each collision, the electrons lose the extra velocity gained.
However, the electric field accelerates the free electrons
continuously and the collisions with atoms prevent their velocity from
becoming abnormally large. Consequently, the electric field causes the free
electrons to move towards the positive terminal of the source with a small
constant velocity, which is called drift
velocity.
Therefore, the application of the potential difference or
voltage across the conductor made the free electrons flow in a specific
direction with a constant velocity. As a result, the net average velocity of all
the electrons in the conductor is not zero, hence an electric current is
established in the conductor.
Hence, here we have thoroughly discussed how the electric current flows through a metallic conductor when a potential difference is applied across it.
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