# Circular motion in a field

A charge moving at right angles to a uniform field follows a circle of radius r = m v / (q B).

Physics (university) · Part 08: Circuits and magnetism · Card 11 of 12 · Last updated 2026-10-19

## Analogy

Mass spectrometers sort ions by this radius.

## Example

**Electron circle**

r = m v / (q B)
= 9.11e-31 x 1e6 / (1.6e-19 x 1e-3)
= 5.7e-3 m

## In practice

An electron at 1e6 m/s in 1 mT circles with radius 5.7 mm.

## Practice

### Flashcards

- **What is the radius of a charge's path in a magnetic field?** r = mv/(qB).

### Interview questions

**Explain why a charged particle in a uniform magnetic field moves in a circle and derive the radius.**

- Force is at right angles to velocity
- Magnetic force provides the centripetal force
- qvB = mv^2/r gives r = mv/qB

## Questions people ask

### How does a mass spectrometer work?

Ions are sped up through a voltage, then enter a magnetic field and follow a circle with radius r = mv/(qB). Heavier ions curve in bigger circles, so they land at different spots on a detector. Measuring where they land gives each ion's mass.

### Why do auroras form near the poles?

Charged particles from the Sun spiral along Earth's magnetic field lines. The lines funnel toward the poles, where the particles hit atoms high in the air. The atoms release light, giving green and red curtains that we call the northern and southern lights.

## Related concepts

- [Magnetic force on a charge](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-10)
- [Magnetic field](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-8)
- [Field of a long straight wire](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-9)
- [Force on a current-carrying wire](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-12)

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