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

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