Electricity uncovered: see the invisible

Electric fields can't be seen, but they push and pull on every charge. Place charges, watch the field they make, measure it, and then follow the current around a real circuit.

Under 15Rub a balloon on your hair and it sticks to the wall: that's static electricity. Things can carry a positive or negative charge. Opposites pull together, and the same kinds push apart. The yellow lines show which way a tiny positive charge would be pushed. Drag the red and blue charges around and watch the lines change! Lower down, close the switch to make electricity flow round a circuit.
20+ · going deeperThe field is E = −∇V with V = Σ kqi/|r − ri|, and Gauss's law ∮E·dA = Qenc/ε₀ is why the number of lines leaving a charge is proportional to q. This 2-D view shows a slice through a 3-D field (1/r² falloff), not the field of infinite line charges (which would fall as 1/r). The far field of a dipole falls as 1/r³ with dipole moment p = qd. In the circuit, drift speed vd = I/(nAe) is ~0.1 mm/s in copper, while the signal travels at a large fraction of c.
1 · Discover2 · Charges lab3 · Understand4 · Potential5 · Circuit6 · Challenges7 · Test yourself

1Discover

Every charge surrounds itself with an electric field, the force a small positive "test" charge would feel at each point, divided by that test charge. Like charges repel and unlike charges attract. We draw the field with field lines: they start on positive charges, end on negative ones, point the way a positive test charge would be pushed, and crowd together where the field is strong. Field lines are a picture of the field, not physical objects: the field exists everywhere, between the lines too.

2Charges lab & field explorer

Drag a charge to move it. Click empty space to measure the field there. Drag the small yellow test charge to feel the force on it.

Start from

Charges

Show

Scale: one grid square = 50 cm. Charges in microcoulombs (μC). k = 8.99 × 10⁹ N m²/C².

3Understand

Coulomb's law gives the field of one point charge q at distance r. It points away from a positive charge and towards a negative one:

E = k |q| / r²

With several charges, the fields simply add as vectors (superposition):

E = E₁ + E₂ + E₃ + …

The force on a test charge q₀ is F = q₀ E. The field's direction is defined as the direction of the force on a positive test charge. A negative charge placed there would be pushed the opposite way.

This simulation calculates the field exactly from Coulomb's law and superposition for point charges in a plane. Field lines are traced by following the field direction step by step, with the number of lines from each charge proportional to its size.

4Electric potential

Tick Equipotential lines above. Each line joins points with the same potential V = Σ k q / r (in volts). Two markers, A and B, are on the workspace: drag them around. Moving a charge q₀ from A to B changes its potential energy by ΔU = q₀ (VB − VA).

Field lines always cross equipotentials at right angles. Moving along an equipotential takes no work (ΔV = 0), so the field can have no component along it: the field must point straight across, towards lower potential.

5A simple circuit

Switch

Show the flow of

Current I = V / R0 A
Power P = V I0 W

Ideal battery, wires and meters (no internal resistance). Conventional current is the direction a positive charge would flow: out of the + terminal. In metal wires the moving charges are electrons, which drift the opposite way, and very slowly (around a millimetre per second). The dots are an illustration of the direction and of how the current grows with V and shrinks with R, not of the real drift speed.

6Challenges

7Test yourself