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Formulas

Lorentz Force

Force on a charged particle due to electric and magnetic fields.

Physics
Subject
Electricity and Magnetism
Sub Subject
Magnetic Fields
Chapter
Force on a Charge
Topic

Lorentz Force

📊 advanced
$$\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$$
Force on a charged particle due to electric and magnetic fields.
Variables & Units
$\mathbf{F}$
Force vector
Unit: $\text{N}$
$q$
Electric charge
Unit: $\text{C}$
$\mathbf{E}$
Electric field
Unit: $\text{N/C}$ or $\text{V/m}$
$\mathbf{v}$
Velocity vector
Unit: $\text{m/s}$
$\mathbf{B}$
Magnetic field
Unit: $\text{T}$ (tesla)
Key Information
📐 Derived From
Maxwell's equations and empirical observations.
💡 Example
Electron in a uniform $\mathbf{B}$ perpendicular to $\mathbf{v}$: circular motion with $r = mv/(qB)$.
🔧 Applications
Mass spectrometry, cyclotrons, Hall effect sensors.
⚠️ Constraints
Classical, non-relativistic ($v \ll c$).

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