Magnetic field

• Introduction
  • Units
  • Lorentz force law
• Cyclotron
• Sources

Introduction

Units

The magnetic field is measured in SI units by the Tesla. It can also be measured by the Gauss (1 Tesla = 10,000 Gauss).

It can also be measured in Weber per meter squared (A weber is the measure of magnetic flux).

Lorentz force law

The Lorentz force law defines both the electric and magnetic fields:

Since $F = qvB$, B is a vector perpendicular to both F and q.

Cyclotron

A cyclotron is a particle accelerator that uses a magnetic force to make moving charges move in a circular motion. This is because the magnetic force acts perpendicular to the direction of motion, “bending” the path towards the center.

An alternating electric field is applied at the “dees” of the cyclotron (two hollow electrodes opposite from each other), which causes the particles to accelerate – they move faster and faster. The particles then move in a spiral path.

The electric field is tuned to the cyclotron frequency (or cyclotron resonance frequency), which is defined as:

$\omega = \frac{qB}{m}$ or $f = \frac{qB}{2\pi m}$

The cyclotron frequency is found by equating the centripetal force and the magnetic Lorentz force:

Sources

• Magnetic Field
• Cyclotron
• Cyclotron (Youtube)