Electron Drift Velocity

Contents

The electron moves at the Fermi speed, and has only a tiny drift velocity superimposed by the applied electric field.

Suppose that in a conductor, the number of free electrons available per m3 of the conductor material is n and let their axial drift velocity be ν metres/second.

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In time dt, distance travelled would be ν × dt.

If A is area of cross-section of the conductor, then the volume is νAdt and the number of electrons contained in this volume is νA dt.

Obviously, all these electrons will cross the conductor cross-section in time dt.

If e is the charge of each electron, then total charge which crosses the section in time dt is dq = nAeν dt.

Since current is the rate of flow of charge, it is given as

i = dq / dt

=nAeν dt/dt

∴ i = nAeν

Current density, J = i/A = ne ν ampere/metre2

Assuming a normal current density J = 1.55 × 10^6 A/m2, n = 10^29 for a copper conductor

and e = 1.6 × 10−19 coulomb, we get

1.55 × 10^6 = 10^29 × 1.6 × 10^−19 × ν ∴ ν = 9.7 × 10^−5 m/s = 0.58 cm/min

It is seen that contrary to the common but mistaken view, the electron drift velocity is rather very

slow and is independent of the current flowing and the area of the conductor.

Question:

A conductor material has a free-electron density of 10^24 electrons per metre^3.

When a voltage is applied, a constant drift velocity of 1.5 × 10^−2 metre/second is attained by the

electrons. If the cross-sectional area of the material is 1 cm^2, calculate the magnitude of the current.

Electronic charge is 1.6 × 10^−19 coulomb.

The magnitude of the current is

i = nAeν amperes

Here, n = 1024 ; A = 1 cm2 = 10^−4 m2

e = 1.6 × 10^−19 C ; v = 1.5 × 10^−2 m/s

∴ i = 10^24 × 10^−4 × 1.6 × 10^−19 × 1.5 × 10^−2 = 0.24 A

Charge Velocity and Velocity of Field Propagation

The speed with which charge drifts in a conductor is called the velocity of charge. its value is quite low, typically fraction of a metre per second.

However, the speed with which the effect of e.m.f. is experienced at all parts of the conductor
resulting in the flow of current is called the velocity of propagation of electrical field.

It is independent of current and voltage and has high but constant value of nearly 3 × 10^8 m/s.

Question 2

Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross-section 1 cm2 and length 10 km. Free electron density of copper = 8.5 × 10^28 per m^3. How long will it take the electric charge to travel from one end of the conductor to the other?
Solution. i = neAν or ν = i/neA
∴ ν= 1/(8.5 × 10^28 × 1.6 × 10^−19 × 1 × 10−4) = 7.35 × 10^−7 m/s = 0.735 μm/s
Time taken by the charge to travel conductor length of 10 km is
t = distance/ velocity
= (10×10^3)/(7.35 x10^−7)
= 1.36 × 10^10 s
Now, 1 year = 365 × 24 × 3600 = 31,536,000 s
t = 1.36 × 10^10/31,536,000 = 431 years

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1.Electron-Mass of electron, Charge of electron, Speed of Electron, value of electron

2. Electron Drift Velocity

3. Mass of Electron, proton, neutron|Charge of electron and Proton