## Summary

- Magnetic fields exert a force on a moving charge
*q*, the magnitude of which is\(F=qvB\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta ,\)

where \(\theta \) is the angle between the directions of \(v\) and \(B\).

- The SI unit for magnetic field strength \(B\) is the tesla (T), which is related to other units by
\(1\text{ T}=\cfrac{\text{1 N}}{\text{C}\cdot \text{m/s}}=\cfrac{\text{1 N}}{\mathrm{A\cdot m}}.\)

- The
*direction*of the force on a moving charge is given by right hand rule 1 (RHR-1): Point the thumb of the right hand in the direction of \(v\), the fingers in the direction of \(B\), and a perpendicular to the palm points in the direction of \(F\). - The force is perpendicular to the plane formed by \(\mathbf{\text{v}}\) and \(\mathbf{\text{B}}\). Since the force is zero if \(\mathbf{\text{v}}\) is parallel to \(\mathbf{\text{B}}\), charged particles often follow magnetic field lines rather than cross them.

## Glossary

### right hand rule 1 (RHR-1)

the rule to determine the direction of the magnetic force on a positive moving charge: when the thumb of the right hand points in the direction of the charge’s velocity \(\mathbf{\text{v}}\) and the fingers point in the direction of the magnetic field \(\mathbf{\text{B}}\), then the force on the charge is perpendicular and away from the palm; the force on a negative charge is perpendicular and into the palm

### Lorentz force

the force on a charge moving in a magnetic field

### tesla

T, the SI unit of the magnetic field strength; \(\text{1 T}=\cfrac{\text{1 N}}{\mathrm{A\cdot m}}\)

### magnetic force

the force on a charge produced by its motion through a magnetic field; the Lorentz force

### gauss

G, the unit of the magnetic field strength; \(\text{1 G}={\text{10}}^{–4}\phantom{\rule{0.25em}{0ex}}\text{T}\)