EMG-08

Lorentz force

F = q (E + v B) for perpendicular v and B.

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Charged particlesLorentz 1892Heaviside

Governing equation

\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})

where

q: Charge (µC)
E: Electric field (N/C)
v: Speed (m/s)
B: Magnetic field (mT)
F: Force magnitude (N)

Lecture brief

Historical brief

Coulomb, Gauss, Ampère, Faraday and Maxwell (1861–65) unified charge, current and light. The lab computes fields, induction, Poynting flux and the electromagnetic wave in SI. This sheet (EMG-08 — Lorentz force) is the form associated with Lorentz 1892 · Heaviside. Working symbols: $q$ , $E$ , $v$ , $B$ $\rightarrow$ $F$ . The Lorentz force is the operational definition of the fields E and B acting on a point charge.

Purpose

Purpose: compute

F

from

q

E

v

B

in Electromagnetism via

\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})

F = q (E + v B) for perpendicular v and B. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

q = 1.500\,\mathrm{\mu C}

E = 200.000\,\mathrm{N/C}

v = 40.000\,\mathrm{m/s}

B = 5.000\,\mathrm{mT}

, the governing relation

\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})

yields

F = 3.003e-4\,\mathrm{N}

. v perpendicular to B so |v×B| = v B; E parallel to F. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Charge q1.5 µCElectric field E200 N/CSpeed v40 m/sMagnetic field B5 mT

Outputs

Force magnitude F0.0003 N

Reading speed

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Narration of this film

v perpendicular to B so |v×B| = v B; E parallel to F.

The Lorentz force is the operational definition of the fields E and B acting on a point charge.

Reading speed

Watch on YouTube