Charge in a Circular Orbit
A single charge going round a loop is a current: it passes any fixed point on the orbit once per revolution. Change the radius and the speed and watch the equivalent current follow, with the electron in the Bohr hydrogen atom available as a preset.
How to use this simulation
- Drag the radius slider to widen or tighten the orbit at fixed speed
- Drag the speed slider to change how often the charge comes round
- Press Bohr hydrogen to jump to the ground-state radius and orbital speed
- Watch the marked point on the orbit register each pass as one crossing
What to look for
- Halving the radius at constant speed doubles the frequency and doubles the current
- Doubling the speed at constant radius does the same thing for the same reason
- The current depends on r and v only through the ratio v/r, never on either alone
- A single charge produces a perfectly steady average current even though it is only there once a lap
- The Bohr preset lands in the milliamp range — a surprisingly ordinary current for one electron
The physics behind it
If a charge Q completes one orbit in a period T, it crosses any chosen point once per period, so the average current there is I = Q/T = Qf. Substituting the orbital relations f = v/2πr and ω = 2πf gives the chain I = Qf = Qv/2πr = Qω/2π — three ways of writing the same thing. For the ground state of hydrogen, an electron orbiting at about 2.2 × 10⁶ m/s at a radius of 5.3 × 10⁻¹¹ m gives a current of roughly one milliamp.