Physics » Magnetism » Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field

# Summarizing Magnetic Field Strength

## 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; $$\text{1 G}={\text{10}}^{–4}\phantom{\rule{0.25em}{0ex}}\text{T}$$