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Formulas

Magnetic Force on Moving Charge

Force on a charged particle moving in a magnetic field.

Physics
Subject
Electricity and Magnetism
Sub Subject
Magnetic Fields
Chapter
Magnetic Force
Topic

Magnetic Force on Moving Charge

📊 intermediate
$$F = qvB\sin\theta$$
Force on a charged particle moving in a magnetic field.
Variables & Units
$F$
Magnetic force magnitude
Unit: $\text{N}$
$q$
Charge
Unit: $\text{C}$
$v$
Speed
Unit: $\text{m/s}$
$B$
Magnetic field strength
Unit: $\text{T}$
$\theta$
Angle between velocity and field
Unit: $\text{rad}$ or $^\circ$
Key Information
📐 Derived From
Lorentz force law
💡 Example
Electron ($q=1.6\times10^{-19}\,\text{C}$) at $v=10^6\,\text{m/s}$ perpendicular to $B=0.1\,\text{T}$: $F = (1.6\times10^{-19})(10^6)(0.1)\sin90^\circ = 1.6\times10^{-14}\,\text{N}$.
🔧 Applications
Cyclotrons, mass spectrometers, cathode ray tubes
⚠️ Constraints
Non-relativistic speeds, uniform field

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