Question

This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

Hint:

Analogy: Think of a pipe completely packed full of marbles. Pushing one marble in at one end immediately pushes a marble out at the far end, even though individual marbles move slowly.

Answer 1

Concept:
• Drift velocity $v_d$ is the actual physical speed at which individual electrons drift along the wire length.

• Electric field establishment throughout circuit occurs via electromagnetic wave propagation.

Step 1: Explanation
When a circuit switch is closed, an electric field is established across every section of the conducting wire almost instantaneously.
The electric field propagates through the wire at the speed of electromagnetic waves in a medium, which is nearly equal to the speed of light $c \approx 3 \times 10^8 \text{ m/s}$.

Step 2: Mechanism
Electric current is not caused by a single electron traveling all the way from source to appliance.
Instead, free electrons are already present densely everywhere throughout the entire volume of conducting wire ($n \approx 10^{28} \text{ m}^{-3}$).
As soon as the electric field reaches every point along the conductor, all free electrons across the entire circuit begin drifting simultaneously at their respective positions.

Step 3: Conclusion
Current is established almost instantly because the electric field travels through the wire at light speed, initiating drift motion of electrons throughout the entire loop at the same instant.