EMG-25

Lorentz force

Perpendicular qvB.

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GoverningLorentz force

Governing equation

F=qvB

$v \in \left[100, 3\times 10^{6}\right]$

where

q: q (e)
v: v (m/s)
B: B (T)
F: Lorentz force (pN)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

F=qvB

$v \in \left[100, 3\times 10^{6}\right]$

$v = 100$ $F = 3.2\times 10^{-6}$

Along the curve

②

Domain of the variable — blue

v_{\min} = 100,\quad v_{\max} = 3\times 10^{6}

$v \in \left[100, 3\times 10^{6}\right]$

$v = 100$ $v = 100$

Along the curve

③

Response curve — green

F=qvB

$v \in \left[100, 3\times 10^{6}\right]$

$v = 100$ $F = 3.2\times 10^{-6}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}F}{\mathrm{d}v}

$v \in \left[100, 3\times 10^{6}\right]$

$v = 18967.3$ $F^{\prime} = 3.2\times 10^{-8}$

Along the curve

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-25 — Lorentz force) is the form associated with Lorentz force. Working symbols: $q$ , $v$ , $B$ $\rightarrow$ $F$ . Perpendicular qvB. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

F

from

q

v

B

in Electromagnetism via

F=qvB

Perpendicular qvB. 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 = 1.000\,\mathrm{e}

v = 100000.000\,\mathrm{m/s}

B = 0.200\,\mathrm{T}

, the governing relation

F=qvB

yields

F = 0.003\,\mathrm{pN}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

q q1 ev v100000 m/sB B0.2 T

Outputs

Lorentz force F0.003 pN

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Perpendicular qvB. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube