Gyro Radius Closes Force Balance - Plasma Physics: Debye Shielding, Gyromotion, and Collective Oscillations Step by Step

A gyro radius is accepted only when magnetic and centripetal forces match. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Centripetal force closes the orbit

Mass 8 kilograms, speed 3 meters per second, and radius 6 meters give centripetal force 12 newtons.

\frac{mv^2}{r}=\frac{8\cdot 3^2}{6}=12\ \text{N}

The same force is the magnetic force

The magnetic force is also 12 newtons, so the radius closes the force balance.

12\ \text{N}=12\ \text{N}