Gyrolla
Cyclotron Motion / Lorentz Force Physics
Gyrolla is a Pixelated Physics law character, one of our forces designs. In a uniform magnetic field a slow charge circles at a fixed frequency: faster ones make bigger circles in the same lap time. This is a 3" × 3" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.
Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days
One equation · 60 seconds · one try · once a day.
Details
Size3″ × 3″
3″ × 3″ kiss-cut sticker.
Shipping
Shipping calculated at checkout by destination. Printed to order for you.
Returns & replacements21 days
Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.
Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.
The physics
A magnetic field bends a charged particle into a circle without changing its speed. Faster particles make bigger circles, but each lap takes the same time, so the cyclotron frequency depends only on charge, mass and field. That is what makes the cyclotron accelerator work.
Equations
| Symbol | Meaning | Unit |
|---|---|---|
| \(q\) | charge of the particle | \(\mathrm{C}\) |
| \(v\) | speed perpendicular to the field | \(\mathrm{m/s}\) |
| \(B\) | magnetic flux density | \(\mathrm{T}\) |
| \(m\) | mass of the particle | \(\mathrm{kg}\) |
| \(r\) | radius of the circle | \(\mathrm{m}\) |
| \(f_c\) | cyclotron frequency, laps per second (non-relativistic; at high energy it falls by 1/γ) | \(\mathrm{Hz}\) |
Sources
- Lawrence & Livingston (1932) The Production of High Speed Light Ions Without the Use of High Voltages, Phys. Rev. 40, 19 (opens in a new tab)
- NobelPrize.org — The Nobel Prize in Physics 1939 (Ernest Lawrence, for the invention and development of the cyclotron) (opens in a new tab)
- NIST CODATA — proton charge to mass quotient e/m_p (gives f/B = 15.245 MHz/T) (opens in a new tab)
Source Lawrence, E. O.; Livingston, M. S. (1932). The Production of High Speed Light Ions Without the Use of High Voltages. Physical Review 40, 19–35.doi.org/10.1103/PhysRev.40.19 (opens in a new tab)