EMG-22

Parallel-plate C

Vacuum parallel plate.

Reading speed

GoverningParallel-plate C

Governing equation

C=\\varepsilon_0 A/d

$d \in \left[0.1, 10\right]$

where

A: A (cm²)
d: d (mm)
C: Parallel-plate C (pF)

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

C=\\varepsilon_0 A/d

$d \in \left[0.1, 10\right]$

$d = 0.1$ $C = 177.1$

Along the curve

②

Domain of the variable — blue

d_{\min} = 0.1,\quad d_{\max} = 10

$d \in \left[0.1, 10\right]$

$d = 0.1$ $d = 0.1$

Along the curve

③

Response curve — green

C=\\varepsilon_0 A/d

$d \in \left[0.1, 10\right]$

$d = 0.1$ $C = 177.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}C}{\mathrm{d}d}

$d \in \left[0.1, 10\right]$

$d = 0.162$ $C^{\prime} = -788.7$

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-22 — Parallel-plate C) is the form associated with Parallel-plate C. Working symbols: $A$ , $d$ $\rightarrow$ $C$ . Vacuum parallel plate. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

C

from

A

d

in Electromagnetism via

C=\\varepsilon_0 A/d

Vacuum parallel plate. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 20.000\,\mathrm{cm^{2}}

d = 1.000\,\mathrm{mm}

, the governing relation

C=\\varepsilon_0 A/d

yields

C = 17.708\,\mathrm{pF}

. 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

A A20 cm²d d1 mm

Outputs

Parallel-plate C C17.708 pF

Reading speed

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Narration of this film

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

Vacuum parallel plate. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube