Mean drift velocity — OCR A-Level Physics
Test yourself on Mean drift velocity with OCR A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Mean drift velocity explained
In a conductor, charge carriers move randomly with high speeds but with no net displacement until an electric field is applied.
Read the full explanation
The field gives each carrier a small average velocity along the conductor, called the mean drift velocity v. The current is I = nAvq, where n is the number density of charge carriers, A is the cross-sectional area, v is the mean drift velocity and q is the charge on each carrier. For copper, n is about 8.5 × 10²⁸ m⁻³, so a current of 1 A in a wire of cross-sectional area 1 × 10⁻⁶ m² gives v = I ÷ (nAq) ≈ 7 × 10⁻⁵ m s⁻¹, a fraction of a millimetre per second. The random thermal speeds are much larger, around 10⁵ m s⁻¹, but average to zero.
(b) I = Anev , where n is the number density of charge carriers
This equation links current to the microscopic motion of charge carriers. I is the current in amperes, A is the cross-sectional area of the conductor in m², n is the number density of charge carriers (number per m³), e is the elementary charge 1.60 × 10⁻¹⁹ C, and v is the mean drift velocity in m s⁻¹. Rearranged, v = I / (Ane). A useful check is that Anev has units m² × m⁻³ × C × m s⁻¹ = C s⁻¹ = A. In a multiple-choice question you may be asked to find v, n or A, or to predict how v changes when A doubles at constant current: v halves. Remember n is a number density, not a mass density, and e is the charge on one carrier, not the total charge.
(c) distinction between conductors, semiconductors and insulators in terms of n.
The three classes of material are distinguished by the number density n of charge carriers available to move. In a conductor such as copper, each atom contributes roughly one free electron, so n is very large, of order 10²⁸ to 10²⁹ m⁻³, and a small drift velocity gives a large current. In an insulator such as polythene, almost all electrons are bound to atoms, so n is extremely small and negligible current flows. A semiconductor such as silicon has a much smaller n than a metal, typically 10¹⁶ to 10¹⁹ m⁻³ at room temperature, but n rises steeply with temperature as more electrons are freed, so its resistance falls. Since I = Anev, at a fixed current a smaller n requires a larger drift velocity.
Your focus
- Define mean drift velocity and describe how it arises from an applied electric field.
- Apply the equation I = nAvq to calculate current, drift velocity, area or number density.
- Explain why the mean drift velocity is much smaller than the random thermal speed of charge carriers.
Show all 9 objectives
- Recall and apply I = Anev to calculate current, area, number density or mean drift velocity.
- Identify the unit and physical meaning of each symbol in the equation.
- Use proportionality to predict how mean drift velocity changes with cross-sectional area or number density at constant current.
- Distinguish conductors, semiconductors and insulators by the number density of charge carriers.
- Relate differences in n to the current carried at a given mean drift velocity.
- Explain how temperature changes n in a semiconductor and the resulting change in resistance.
Mean drift velocity exam tips
Marking Points
- Mean drift velocity is the average velocity of charge carriers along a conductor due to an applied electric field.
- The relationship is I = nAvq, where n is the number density of charge carriers, A is the cross-sectional area, v is the mean drift velocity and q is the charge on each carrier.
- Carriers also have much larger random thermal speeds, but these average to zero and do not contribute to the current.
- For a given current, a smaller cross-sectional area or a smaller number density gives a larger mean drift velocity.
- Typical values of mean drift velocity in metals are of the order of 10⁻⁵ to 10⁻⁴ m s⁻¹, far smaller than the random thermal speeds.
- States I = Anev and identifies each symbol with its unit: I in A, A in m², n in m⁻³, e in C, v in m s⁻¹.
- Rearranges correctly to v = I / (Ane) or n = I / (Aev) as required by the question.
- Uses e = 1.60 × 10⁻¹⁹ C for electrons or the appropriate carrier charge for ions.
- Applies proportionality reasoning, for example at constant I, doubling A halves v because v ∝ 1/A.
- Checks that the product Anev has units of current, confirming dimensional consistency.
- States that conductors have a very high number density of charge carriers, insulators a very low one, and semiconductors an intermediate value.
- Links the size of n to the current produced for a given drift velocity through I = Anev.
- Explains that in semiconductors n increases with temperature, so resistance decreases.
- Recognises that in metals n is approximately constant with temperature, while lattice vibrations dominate resistance.
- Uses order-of-magnitude values, for example n ≈ 10²⁸ m⁻³ for copper and n ≈ 10¹⁶ m⁻³ for intrinsic silicon.
Examiner Tips
- 💡Rearrange I = nAvq for the quantity required before substituting values, and check that all units are SI.
- 💡Remember that for electrons q = 1.60 × 10⁻¹⁹ C, and use the magnitude when calculating v.
- 💡If a question gives the number of carriers per unit volume, use it directly as n; if it gives the total number, divide by the volume of the conductor.
- 💡Write the rearranged equation before substituting numbers so the examiner can follow your method.
- 💡Convert all lengths to metres and areas to m² at the start of the calculation.
- 💡Use the unit check Anev → C s⁻¹ = A to confirm you have not inverted the relationship.
- 💡When comparing two wires, reason with ratios rather than recalculating from scratch.
- 💡Quote approximate orders of magnitude for n to support your comparison.
- 💡Link every statement about n back to I = Anev so the physics reasoning is explicit.
- 💡For temperature questions, separate the effect on n from the effect on lattice vibrations.
- 💡Use the phrase 'number density of charge carriers' rather than 'number of electrons' to stay precise.
Common Mistakes
- Confusing mean drift velocity with the speed at which the electrical signal travels: the signal propagates much faster than the carriers drift.
- Using the cross-sectional area in cm² without converting to m²: the equation requires SI units, so convert 1 cm² to 1 × 10⁻⁴ m².
- Forgetting that n is the number density of charge carriers per cubic metre, not the total number of carriers in the wire.
- Treating n as a mass density in kg m⁻³; n is a number density of charge carriers per m³, so it is a pure number per unit volume.
- Using e as the total charge or as 1 C; e is the elementary charge 1.60 × 10⁻¹⁹ C carried by one electron or proton.
- Forgetting to convert area from mm² or cm² to m² before substituting; for example 1 mm² = 1 × 10⁻⁶ m².
- Assuming v is the speed of individual electrons along the wire; v is the mean drift velocity, which is very small compared with random thermal speeds.
- Saying insulators have no charge carriers at all; they have very few mobile carriers, which is why the current is negligible rather than exactly zero.
- Confusing number density n with resistivity or resistance; n is a property of the material's carrier population, not a direct measure of opposition to current.
- Claiming n in a metal increases greatly with temperature; in a metal n is roughly constant and the resistance rise comes mainly from increased lattice vibration.
- Assuming a semiconductor behaves like a metal because both conduct; a semiconductor's conductivity depends strongly on temperature and on doping.