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Formulas

Magnetic Force on a Moving Charge

Calculates the force exerted by a magnetic field on a particle with charge $q$ moving with velocity $v$.

Physics
Subject
Electromagnetism
Sub Subject
Magnetic Effects of Current
Chapter
Lorentz Force
Topic

Magnetic Force on a Moving Charge

📊 intermediate
$$F = qvB \sin \theta$$
Calculates the force exerted by a magnetic field on a particle with charge $q$ moving with velocity $v$.
Variables & Units
$F$
Magnetic Force
Unit: Newton ($N$)
$q$
Electric charge
Unit: Coulomb ($C$)
$v$
Velocity of particle
Unit: $m/s$
$B$
Magnetic field strength
Unit: Tesla ($T$)
$\theta$
Angle between velocity and field
Unit: Degrees/Radians
Key Information
📐 Derived From
Lorentz Force Law: $\vec{F} = q(\vec{v} \times \vec{B})$.
💡 Example
Path of an electron in a cathode ray tube.
🔧 Applications
Mass spectrometers, cyclotrons, and auroras.
⚠️ Constraints
Charge must be moving relative to the magnetic field.

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