19.3 Drift Velocity
19.3.1 Equation for Drift Velocity
Figure 19.5 Drift of electrons in a conductor with uniform cross-sectional area Aproducing an average electric current I
-
Let vd = drift velocity of an electron
n = number of free electrons per unit volume -
In time interval Δt, the distance Δx travelled by an electron is
Δx = vd Δt -
The volume ΔV of length Δx is
ΔV = A vd Δt -
The number N of electrons within the volume ΔV is
N = nΔV -
The total charge Q carried by N electrons is
ΔQ = Ne, where e is the charge of an electron. -
The average current in the conductor is
I = ΔQ / Δt
I = Ne / Δt
I = (nΔV)e / Δt
I = n(A vd Δt)e / Δt
Therefore:
I = A n e vd
or the drift velocity
vd = I / (A n e)
Factors Affecting Drift Velocity
The magnitude of vd depends on the following quantities:
(a) Current
vd ∝ I
The current is dependent on the potential difference V across the conductor and the resistance R of the conductor. Hence, vd is dependent on V and R.
(b) Cross-sectional Area
vd ∝ 1 / A
For a wire with circular cross section:
A = (1/4) π d²
Hence,
vd ∝ 1 / d²
(c) Number Density of Electrons
vd ∝ 1 / n
Effect of Temperature
For a metal, n does not change much when there is a change in temperature. However, for a semiconductor, n increases with temperature. This is because more free electrons and holes are generated when the temperature of the semiconductor increases.
19.3.2 Typical Order of Magnitude of Drift Velocity
1. Drift velocity in metals and semiconductors
(a) In metals, vd ≈ 10−7 – 10−4 m s−1
(b) The value of n for a semiconductor is very much smaller than the value of n for a metal. Hence, we expect vd to be much larger in value. We have vd ≈ 10−2 – 101 m s−1.
2. Instant lighting up of electric bulb
If electrons have such an extremely slow drift velocity in a metal, we may wonder why an electric filament bulb could light up almost instantly when the switch is closed. We might assume that it would take electrons a very long time to reach the bulb and hence lighting it up.
Reasons:
- Free electrons are already present in the bulb filament. There is no need to consider electrons outside the filament at the moment when the switch is closed.
- At the moment when the switch is closed, a p.d. is almost immediately applied across the bulb. The p.d. will produce an electric field which travels at nearly the speed of light through the filament.
- Hence, all the free electrons in the filament immediately experience electric forces acting on them. All start to drift at the same time in the filament, thus instantly producing an electric current. The current in turn produces a heating effect, which causes the bulb to light up almost instantly.
Example 19.2
A current of 1.0 A flows in a copper wire of diameter 1.0 mm. Copper has the following properties:
- density = 8.95 kg m−3
- molar mass = 63.5 g mol−1
(a) Assuming that each copper atom in the wire contributes one free electron, determine the number of free electrons in 1.0 m3 of copper.
(b) Determine the drift velocity of the electrons in the wire.
[Electronic charge = −1.6 × 10−19 C; Avogadro constant = 6.02 × 1023 mol−1]
Answer
(a) Mass of 1.0 m3 of copper
m = ρV
= (8.95)(1) = 8.95 kg (for 1 m3)
Number of free electrons
n / (6.02 × 1023 mol−1) = mass of copper / molar mass
= (8.95 × 103 g) / (0.0635 g mol−1)
n = 8.48 × 1028 m−3
(b) Cross-sectional area of wire
A = 1/4 πd2
= 1/4 π (1.0 × 10−3)2 = 7.85 × 10−7 m2
Drift velocity
vd = I / (neA)
= 1 / [(8.48 × 1028)(1.6 × 10−19)(7.85 × 10−7)]
= 9.4 × 10−5 m s−1
≈ 1 × 10−4 m s−1
Example 19.3 Drift Velocity in Semiconductor
A constant current of 10 μA flows in a piece of germanium of uniform cross-sectional area 5.0 × 10−7 m2. At a certain temperature, the number of free charge carriers per unit volume is 4.0 × 1021 m−3. Assuming that a hole in the germanium behaves like an electron, estimate the drift velocity of the charge carriers.
Answer
Drift velocity
vd = I / (neA)
= 10 × 10−6 / [(4.0 × 1021)(1.6 × 10−19)(5.0 × 10−7)]
= 0.3 × 10−1 m s−1
= 10−2 m s−1
Note
(a) A piece of intrinsic semiconductor does not conduct electricity well because it has a very much higher resistance than a metal of similar size. The current through it is of the order of magnitude of several microampere at room temperature.
(b) The number of free charge carriers n available in unit volume of a piece of intrinsic semiconductor at room temperature is very much lower than the number of electrons found in a metal. For metal, n ~ 1028 m−3 whereas for semiconductor like germanium, n ~ 1021 m−3.
(c) Since vd ∝ 1/n, it means that
vd in semiconductor >> vd in conductor
if the same p.d. is applied across a piece of semiconductor and across a metal of similar size.
Applications of Drift Velocity
Drift velocity plays an important role in understanding how electric current flows in different materials. It has many practical applications in physics, electronics, and engineering.
1. Electrical Conductors
Drift velocity helps explain how electrons move in metallic conductors when an electric field is applied, which is essential for the functioning of electrical wiring systems.
2. Semiconductor Devices
In semiconductors, drift velocity is used to analyze the movement of electrons and holes, which is crucial in the operation of devices such as diodes, transistors, and integrated circuits.
3. Current Density Analysis
Drift velocity is directly related to current density, allowing engineers to design efficient electrical systems by controlling the flow of charge carriers in a material.
4. Electronic Circuit Design
Understanding drift velocity helps in designing circuits by predicting how quickly charge carriers respond to an applied electric field.
5. Power Transmission Systems
Drift velocity is important in analyzing how electric current flows through transmission lines, ensuring efficient delivery of electrical energy over long distances.
6. Plasma Physics and Gas Discharge
In gases and plasma, drift velocity helps describe the motion of charged particles under electric fields, which is important in applications like fluorescent lamps and plasma devices.
7. Microelectronics and Nanotechnology
At very small scales, drift velocity is used to study charge transport in microchips and nanoscale devices, helping improve performance and efficiency.
8. Sensors and Measurement Devices
Drift velocity is applied in designing sensors and instruments that measure electric current and charge movement in various systems.
Conclusion: Drift Velocity
In conclusion, drift velocity is a fundamental concept in understanding the motion of charge carriers in a conductor when an electric field is applied. Although the random motion of electrons is very fast, their net movement in a specific direction, known as drift velocity, is relatively slow.
The concept of drift velocity helps explain how electric current is produced in different materials such as metals and semiconductors. It also shows the relationship between current, charge density, and electric field, which is essential in the study of electrical conduction.
Understanding drift velocity is important in many practical applications, including electronic devices, power transmission systems, and semiconductor technology. It provides a deeper insight into how electrical energy is transferred and controlled in modern electrical and electronic systems.
Overall, drift velocity plays a crucial role in physics and electrical engineering, making it an essential topic for students studying electricity and magnetism.
Frequently Asked Questions (FAQ) – Drift Velocity
1. What is drift velocity?
Drift velocity is the average velocity at which charge carriers such as electrons move through a conductor under the influence of an electric field.
2. What is the formula for drift velocity?
The drift velocity is given by the formula:
vd = I / (nqA)
where I is current, n is the number of charge carriers per unit volume, q is the charge of each carrier, and A is the cross-sectional area.
3. Why is drift velocity very small?
Drift velocity is very small because electrons frequently collide with atoms in the conductor, which slows down their net motion in one direction.
4. What is the direction of drift velocity?
In metals, electrons drift in a direction opposite to the applied electric field due to their negative charge.
5. What is the relation between drift velocity and current?
Electric current is directly proportional to drift velocity. A higher drift velocity results in a greater electric current.
6. What factors affect drift velocity?
Drift velocity depends on the electric field strength, number of charge carriers, temperature, and the nature of the material.
7. What is drift velocity in semiconductors?
In semiconductors, both electrons and holes contribute to drift velocity, moving in opposite directions under an electric field.
8. What is the SI unit of drift velocity?
The SI unit of drift velocity is meter per second (m/s).
9. Why is drift velocity important?
Drift velocity is important because it explains how electric current flows in conductors and is essential in designing electrical and electronic systems.
10. Where is drift velocity used in real life?
Drift velocity is used in electronic devices, semiconductor technology, power transmission, and current analysis in circuits.
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