Question

Answer the following giving reason :
The electron drift speed is estimated to be only a few mm/s for currents in the range of a few amperes. How, then, is the current established almost the instant a circuit is closed ?

Hint:

To intuitively understand this, imagine a long rigid tube perfectly filled end-to-end with ping-pong balls. If you push one ball into the left end, a different ball instantly falls out of the right end. The "signal" travels instantly, even though the specific ball you pushed barely moved!

Answer 1

Concept:
• In a metallic conductor, electric current is physically carried by free electrons moving in a specific direction.
• While the actual physical translation of these electrons (drift velocity) is incredibly slow, the electrical signal propagates in an entirely different manner.
• The signal is established by an electromagnetic field that travels independently of the physical particles.

Step 1: Explain the nature of electron drift
It is entirely physically accurate that individual free electrons move at a microscopic crawl, generally a few millimeters per second (drift speed $v_d$).
This extreme slowness is due to the incredibly dense lattice of metal ions; the electrons suffer billions of chaotic, random collisions every single second, heavily retarding their forward progress.

Step 2: Explain the establishment of the electric field
However, an electric circuit does not operate by patiently waiting for one specific electron to travel all the way from the battery's negative terminal to the positive terminal.
The absolute instant the circuit switch is mechanically closed, an electromagnetic field is established throughout the entire length of the conductor.
This invisible electric field propagates through the wire at nearly the absolute speed of light in a vacuum ($c \approx 3 \times 10^8$ m/s).

Step 3: Connect the field to the macroscopic current
Because the electric field travels almost instantaneously, it reaches every single free electron physically present anywhere in the entire wire at practically the exact same moment.
This rapidly established field instantly exerts an electrostatic force ($F = -eE$) on all the free electrons simultaneously.
As a result, electrons everywhere in the circuit begin their slow drift at the exact same time.

Step 4: Conclusion
Since electrons at the far end of the circuit begin moving simultaneously with those near the battery, the macroscopic electric current is established universally the very instant the switch is closed, despite the extremely slow physical speed of the individual charge carriers.