“The real concept of electron flow in a conductor”

Clearing a fundamental misconception in electricity.

 

Author:
Prof. Kali Chandrakant
              M.Sc., M.Ed., D.C.S.
50+ Years of experience in Physics teaching.

1. Introduction: A common but serious misconception:

     Many students believe that electrons start moving from the negative terminal to the positive terminal only after a battery is connected to a conductor. This idea looks logical at first, but it is scientifically incorrect. Surprisingly, this misconception is found not only among school students, but also among senior secondary and first-year B.Sc. students.

The truth is simple but important:

   Electrons are always in a random motion inside a conductor, even when no battery is connected.

      To clearly understand this, we must patiently look at the microscopic picture of a conductor. Let us proceed step by step.

2. Atomic structure and conductors:

2.1. Atomic structure:

 First consider the atomic structure. Every conductor is made up of atoms.

An atom consists of:

• Electrons (e⁻) – negatively charged
• Protons (p⁺) – positively charged
• Neutrons (n⁰) – electrically neutral

   At the centre of the atom is the nucleus, which contains protons and neutrons. Because of protons, the nucleus is positively charged. Electrons revolve around the nucleus in different energy levels (shells).

   This basic atomic structure plays a crucial role in understanding electrical conduction. Now let us discuss about sodium atom.

 2.2. Sodium atom: Source of free electrons:

Fig.A

   Let us consider sodium metal, which is a good conductor.

• Atomic number of sodium = 11
• Electronic configuration = 2, 8, 1
• Number of valence electrons = 1

    The single electron in the outermost shell is weakly bound to the nucleus. This weak binding is the key reason why sodium can conduct electricity.

      Figure A represents the electronic structure of a sodium atom. Using this structure sodium atom, let us see what changes occurs when large number (of the order 10²² atoms/cm³) of atoms come together to form metal. 

2.3. Formation of a metal crystal:

   When a large number of sodium atoms come together, they arrange themselves in a regular and orderly pattern, forming a crystal lattice.

  This is shown in Fig. B:

• The green spheres represent sodium ions arranged in a crystal lattice.
• The small highlighted entities between them represent free electrons, forming what is called an electron gas or electron sea.

Fig.B

In the sodium metal actually following thing occurs as shown in Fig. C:

• The grey circles represent localised positive sodium ions fixed at lattice points.
• The red symbols represent free electrons, which are not attached to any single atom and move randomly in the space between ions.

Fig.C

As we move farther from the nucleus:

• The attractive force on electrons decreases.
• Hence, the outermost electron experiences the least attraction.

During the formation of the metal crystal:

• The outer electrons become delocalised.
• They are no longer bound to individual atoms,
• Each sodium atom becomes a positively charged Na⁺ ion.
• The valence electrons form a common pool or “sea” of free electrons.

This situation is clearly shown in Fig. B and Fig. C.

3. Free electrons and random motion:

 Inside the metal:

• Positive sodium ions remain at fixed lattice positions (they only vibrate slightly)
• Free electrons move in the space between these ions

These free electrons are in continuous random motion due to:

• Their thermal energy.
• Frequent collisions with vibrating lattice ions.

3.1. Important Observation:

  Even though electrons are moving continuously and randomly, there is no electric current when no battery is connected.

3.2. Why does current not flow?

Because:

   The number of electrons crossing any cross-section in one direction is exactly equal to the number crossing in the opposite direction.

This balanced situation is illustrated in Fig. D.

 4. Why is there no current without a battery?

Fig.D

Let us observe the motion of a single electron.

• Suppose an electron is at point A at a certain instant
• Due to random motion, after time t, it may reach point B
• Each electron follows a different zig-zag and unpredictable path

Since motion is random in all directions:

• The net flow of charge across any cross-section is zero

Hence we conclude:

The random motion of electrons alone does not produce electric current.

5. Effect of applying voltage to a conductor:

  Now let us connect a battery of voltage V across the conductor.

The battery performs two important functions:

• It establishes an electric field inside the conductor
• It supplies energy E = eV to each electron

Due to the electric field, each electron experiences a force:

F = -eE

As a result:

• Electrons acquire a small net motion towards the positive terminal of the battery.

6. Superposition of motions: Random + Drift:

Fig.E

 6.1. It is very important to understand that:

• Random motion does not stop.
• A small directional motion is added.

Thus, each electron now has:

1. Random thermal motion.
2. Slow drift motion towards the positive terminal.

In Figure E:

• Without voltage, an electron moves from A to B in time t.
• With voltage applied, it moves from A to B₁ in the same time t.

The small shift:

BB₁ = S

This shift represents the effect of the electric field.

6.2. Drift velocity (vₑ):

Drift velocity is defined as:

v_d = S/t

   Although electrons move randomly at very high speeds, their drift velocity is extremely small, typically of the order of mm per second.

  Yet, this small drift is sufficient to produce electric current.

7. How is electric current produced?

   Because of drift:

• More electrons cross a given cross-section in one direction
• Let n electrons cross extra in time t
• Total charge flowing:Q = ne
• Hence current:I = Q/t = ne/t

  Therefore:

 The electric current is produced due to the net drift of electrons, not due to their random motion.

8. Direction of current:                   

  In metal wires:

• Electrons drift from the negative terminal to the positive terminal
• Conventional current is defined from positive to negative

   This convention exists for historical reasons. Both descriptions are correct; one refers to negative charge flow, the other to an imagined positive charge flow.

9. Everyday analogy: Ganapati procession:

Consider a Ganapati immersion procession with Lezim players:

• Players performing Lezim → Random motion
• Team standing at one place → No procession
• Team leader gives a forward command → Electric field
• Players continue performing while moving forward → Random + drift motion

Similarly:

• Electrons move randomly
• Battery creates a directional force
• Slow drift produces electric current

10. Final conclusion:

• Free electrons exist in a conductor even without a battery
• Their motion is random and produces no current
• Applying voltage creates an electric field
• Random motion becomes biased
• Net drift of electrons produces electric current

The electric current is not the speed of electrons, but the result of their organised drift.

11. Suggested animation:

For visual understanding of electron flow, refer to the following video:

1. YouTube: Electron Flow in a Conductor
   https://www.youtube.com/watch?v=KprFTxjQAoE