Gyro Field Boundary Closure Scan - Plasma Physics: Debye Shielding, Gyromotion, and Collective Oscillations Step by Step

Gyro radius, force, and turn rate are scanned across a wide field range. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The checked field closes radius and force together

With charge two coulombs, speed three meters per second, mass eight kilograms, and field two tesla, the radius is six meters.

r=\frac{12}{2}=6\ \text{m}

A wide field scan exposes the fractional edge

The same charge, speed, and mass stay fixed. At eight tesla the radius becomes three halves of a meter while force and turn rate rise.

\begin{array}{c|c|c|c}B&r&qvB&\Omega\\1&12&6&\frac{1}{4}\\2&6&12&\frac{1}{2}\\8&\frac{3}{2}&48&2\\\end{array}

Tighter radius is paid for by larger magnetic force

The table keeps both sides of the force balance visible: qvB rises with field while the required circular radius falls.

B\uparrow:\quad qvB\uparrow,\quad r=\frac{mv}{qB}\downarrow