Electric Current & Current Density
Charge on the move, and how it spreads over a cross-section.
Lesson at a glanceShow the key points
- i = dQ/dt (32.1); 1 A = 1 C/s, an SI base unit.
- Direction: the way positive charge moves; opposite to electron motion.
- Current is not a vector; current density j⃗ is: j = i/S (32.2), i = ∫j⃗·dS⃗ (32.3).
- Currents arise from thermionic electrons, ions in solutions, charging capacitors, and conductors in a field.
Until now charges sat still. Let them move and you get an electric current: the thing that lights bulbs, turns motors and runs every circuit.
Electric current
Whenever charge passes from one side of a surface to the other, there is a current through that surface. If charge Q crosses in time Δt, the average current is Q/Δt; the current at an instant is the rate of flow:
The SI unit is the ampere (A): one coulomb per second. It is one of the seven SI base units. The direction of a current is the direction in which positive charge moves; if the carriers are negative, the current points opposite to their motion.
Current density
To describe how current is spread over a cross-section we use a vector, the current density.
If the area is tilted so that its normal makes an angle θ with the flow, only the perpendicular part counts: Δi = jΔS cos θ = j⃗·ΔS⃗. For a finite surface:
In a beam of cross-section 2.0 mm², 3.0 × 10¹⁶ electrons pass any cross-section each second. Find (a) the current, (b) the current density.
An electron moves round a circle of radius 5.0 cm at a steady 2.0 × 10⁶ m/s. What is the current at a point on the circle?
Where currents come from
- A hot metal emits electrons that fly through space: a current through any area they cross.
- In a solution, positive ions drift along a field and negative ions against it; both add to the current along the field.
- While a capacitor charges, charge flows along the connecting wires.
- This chapter: free electrons in a metal, pushed by a field inside the conductor.
- 1i = dQ/dt (32.1); 1 A = 1 C/s; direction = motion of positive charge.
- 2Current is not a vector; current density j⃗ is.
- 3Uniform: j = i/S (32.2); in general i = ∫j⃗·dS⃗ (32.3).
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.