Gyro Radius Field Cross-Scan - Condensed Matter and Plasma Physics Step by Step

A gyro-radius-field cross-scan varies the magnetic field across rows, showing how the gyro radius r_L = m * v_perp / (q * B) tightens as the field grows. The arithmetic is exact only for the stated charge, mass, perpendicular speed, magnetic field, and rows in the ideal uniform-field model. Real plasmas add collisions, nonuniform fields, distribution functions, boundary/sheath effects, calibration, finite precision, and measurement uncertainty.

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

highlighted = computed this step

Gyro radius closes the same force balance

The checked source has field three tesla. With the fixed charge, speed, and mass, radius is four meters and force is eighteen newtons.

r=\frac{12}{3}=4\ \text{m},\quad qvB=18\ \text{N}

A stronger field tightens radius and raises turn rate

Charge, speed, and mass stay fixed. Field increases across the rows, so radius falls while force rises.

\begin{array}{c|c|c|c}B&r&qvB&\text{turn rate}\\2&6&12&\frac{1}{2}\\3&4&18&\frac{3}{4}\\4&3&24&1\\\end{array}