How to play Floating Bead
- Choose a test and read the charges, the mass, or the height wanted on the card.
- Use k·q₁·q₂ ÷ r² = m·g with charges in C, r in m, and m in kg.
- Type your prediction and press Start. The thread lowers the top bead from the top of the tube.
- See where the thread goes slack, and compare it with your orange line or the gray target.
Coulomb's law
Two charges push each other apart if they have the same sign and pull together if they have opposite signs. In 1785 Charles-Augustin de Coulomb measured the force with a torsion balance and found F = k·q₁·q₂ ÷ r², with k = 8.99 × 10⁹ N·m²/C². The force grows with each charge and falls with the square of the distance: half the distance, four times the force. It acts on both charges, equally and in opposite directions. The electric force is enormously stronger than gravity between small things: a few tens of nanocoulombs on two beads a few centimetres apart are enough to hold one up against the whole Earth's pull. That is why a rubbed balloon can lift your hair.
A focused learning model
The beads are small spheres, so they act as point charges, and r is the gap between their centres. The glass is a perfect insulator and the beads lose no charge. The thread's end is lowered steadily from the top of the tube (16 cm) to 0.6 cm in 2 s, slowly enough that the bead is always in balance: the thread pulls m·g − F while that is positive and goes slack exactly where F = m·g. A bead pushed harder than its weight at the top stays against the cap; one too heavy to float rests on the bottom bead. The tube and the gap are to scale; the beads are drawn larger. Answers within 2% are right.