How to play Charge Tug
- Choose a test and read the charges and their places on the card.
- Use F = k·q₁·q₂ ÷ r² for each pair, with charges in C and r in m, and add forces with their directions.
- Type your prediction and press Start. One bead is brought in; the gauges read the forces.
- Compare the gauge with your orange line, or watch whether the third bead stays put.
Forces between charges
Coulomb's law gives the force between two point charges: F = k·q₁·q₂ ÷ r², with k = 8.99 × 10⁹ N·m²/C². Like charges repel and unlike charges attract, and the two forces are always equal and opposite, as Newton's third law says. When there are more than two charges, each pair acts as if the others weren't there, and the forces on a charge add as vectors; on a straight line, that means adding with signs. A third charge between two like charges feels no force where the two pushes cancel, which is nearer the smaller charge because the force falls with the square of the distance. The same law, scaled down to atoms, holds electrons around nuclei and holds molecules together.
A focused learning model
The beads are point charges on a straight, frictionless rod. The moving bead is brought in steadily over 2 s, slowly enough that the gauges read the electric force at every moment, and is then held for 1 s. In the balance test, the third bead is held at your point and let go at 2 s: it counts as balanced within 2% of the balance point, where a little friction holds it; otherwise it is pushed, drawn for 1 s as an illustration rather than a simulation. Arrows show the total force on each bead at a fixed scale per test. Answers within 2% are right.