Drift Velocity Khan Academy Guide
What is Drift Velocity?
Drift velocity is the average velocity that charged particles (usually electrons) achieve in a material when an electric field is applied. Electrons in a wire don't shoot through at the speed of light. They drift. Slowly. Think of it like cars crawling through a parking lot during rush hour.
In any conductor, electrons move randomly at high speeds (around 106 m/s at room temperature). But this motion is chaotic. When you apply a voltage, you add a tiny net movement in one direction. That net movement is the drift velocity.
It's small. Usually on the order of millimeters per second. But it's what carries current through wires.
The Drift Velocity Formula
Here's the equation you need to know:
vd = I / (n × A × q)
Where:
- vd = drift velocity (m/s)
- I = current (amperes)
- n = number of charge carriers per unit volume (m-3)
- A = cross-sectional area of the conductor (m2)
- q = charge of each carrier (coulombs)
You can rearrange this to solve for any variable. If you're hunting for current instead: I = n × A × q × vd
How to Calculate Drift Velocity
The Step-by-Step Process
Let's work through a real example so you see how this plays out.
Problem: A copper wire has a current of 3 amperes flowing through it. The wire has a cross-sectional area of 1 mm2 (that's 1 × 10-6 m2). Copper has approximately 8.5 × 1028 free electrons per cubic meter. Find the drift velocity.
Step 1: Identify your values.
- I = 3 A
- n = 8.5 × 1028 m-3
- A = 1 × 10-6 m2
- q = 1.6 × 10-19 C (electron charge)
Step 2: Plug into the formula.
vd = I / (n × A × q)
vd = 3 / (8.5 × 1028 × 1 × 10-6 × 1.6 × 10-19)
Step 3: Calculate the denominator.
Denominator = 8.5 × 1 × 1.6 × 1028-6-19 = 13.6 × 103 = 1.36 × 104
Step 4: Divide.
vd = 3 / 1.36 × 104 ≈ 2.2 × 10-4 m/s
Answer: The drift velocity is about 0.22 mm/s.
That's it. Slow as hell, but that's how current works.
Drift Velocity vs Current: The Difference
Students confuse these constantly. Stop.
Current is the total charge flowing past a point per second. It's a rate. Measured in amperes. Think of it like the flow rate of water through a pipe (gallons per minute).
Drift velocity is the speed at which the carriers themselves are moving. Think of it like the actual speed of water molecules through that pipe.
A thick pipe can move the same amount of water at a slower molecular speed than a thin pipe. Same with wires. Increase the cross-sectional area, and you can have the same current with a lower drift velocity.
Why This Matters
High drift velocities cause heating. Electrons crashing into atoms release energy. This is why power lines heat up. This is why your phone charger gets warm. The faster electrons have to shove through, the more collisions happen.
Also worth knowing: drift velocity is inversely proportional to cross-sectional area. Double the wire thickness, halve the drift velocity for the same current.
Factors That Affect Drift Velocity
Three things control how fast electrons drift in a material:
- Current magnitude — More current means higher drift velocity. Direct relationship.
- Material properties (n) — Different materials have different numbers of free electrons. Copper has many. Insulators have almost none. This is why conductivity varies.
- Cross-sectional area (A) — Thicker wire = lower drift velocity for the same current. Inverse relationship.
Temperature also plays a role indirectly. As temperature increases, atoms vibrate more, which increases resistance and effectively slows the net movement of electrons even if the theoretical drift velocity stays the same.
Comparing Electron Velocity Concepts
This table clears up the confusion between the different "speeds" you'll encounter:
| Concept | Typical Value | Description |
|---|---|---|
| Thermal velocity | ~106 m/s | Random motion of electrons at room temperature |
| Drift velocity (copper, typical) | 10-4 to 10-3 m/s | Net movement due to applied voltage |
| Signal propagation speed | ~108 m/s | Speed of the electromagnetic wave in the wire |
The signal reaches the other end of a wire almost instantly. But the electrons themselves barely move. That's the key distinction.
Getting Started on Khan Academy
If you want to learn this properly on Khan Academy, here's how to find it:
- Search for "Electric current and drift velocity" in the search bar
- Look under the Physics section, specifically Electric charge and electric force
- The video walks through the conceptual explanation before jumping into calculations
What to do before you start:
- Make sure you understand what current is (charge per unit time)
- Know the electron charge: 1.6 × 10-19 C
- Be comfortable with scientific notation
Watch the video once without pausing. Then rewatch while taking notes. Try the practice problems without looking at the solutions first. If you get stuck, rewind. This isn't complicated once the formula clicks.
The common mistakes students make:
- Forgetting to convert units (mm2 to m2 trips people up)
- Using the wrong value for electron charge (positive vs negative sign)
- Confusing current with drift velocity
Fix those three things and you'll never bomb a drift velocity problem again.