Explain electromagnetic waves

projects/em_waves/scenes.py

The question

How do changing electric and magnetic fields sustain a wave?

This project demonstrates how a long technical explanation can remain one continuous spatial argument instead of becoming disconnected slides.

Capabilities demonstrated

• Physics notation and Maxwell’s equations
• Long-form tape structure
• Flex rows and columns
• Sectioned explanation
• Mathematical 3D surface
• Camera transition between flat and spatial content

Establish the phenomenon

builder = CanvasBuilder(title="Electromagnetic Waves")
tape = builder.add_tape("main")

tape.add_heading(
    "Electromagnetic waves",
    style={"align": "center", "margin-bottom": 0.5},
)
tape.add_body(
    "Light, radio, and X-rays are the same phenomenon: "
    "oscillating electric and magnetic fields that travel "
    "through space.",
    style={"margin-bottom": 0.7},
)

The project begins in plain language before introducing notation.

Present related quantities together

tape.add_flex_row(
    [
        tape.text_spec(
            "Electric field E",
            style={"width": 2.6, "align": "center"},
        ),
        tape.text_spec(
            "⟷ coupled",
            style={"width": 1.6, "align": "center"},
        ),
        tape.text_spec(
            "Magnetic field B",
            style={"width": 2.6, "align": "center"},
        ),
    ],
    gap=0.3,
    justify_content="center",
)

A row communicates coupling more directly than three unrelated reveals.

Build the equation group

tape.add_flex_column(
    [
        tape.math_spec(r"\nabla \cdot \vec{E} = 0"),
        tape.math_spec(r"\nabla \cdot \vec{B} = 0"),
        tape.math_spec(
            r"\nabla \times \vec{E}"
            r" = -\frac{\partial \vec{B}}{\partial t}"
        ),
        tape.math_spec(
            r"\nabla \times \vec{B}"
            r" = \mu_0 \varepsilon_0"
            r" \frac{\partial \vec{E}}{\partial t}"
        ),
    ],
    gap=0.35,
    align_items="center",
)

The equations remain separate elements even though the flex column groups them visually.

Create a 3D visual break

builder.add_3d(
    r"z = \sin(x)\cos(y)",
    pitch=50,
    style={
        "width": 5.2,
        "align": "center",
        "margin-bottom": 0.5,
    },
)

tape.add_body(
    "A snapshot of a wave-like surface.",
    after_3d=True,
)

The 3D moment should reinforce the spatial idea of a field rather than serve as unrelated decoration.

Long-form organization

The complete project progresses through:

1. Physical intuition
2. Maxwell’s equations
3. The wave equation
4. A plane-wave form
5. A spatial visual break
6. The electromagnetic spectrum
7. Summary

This structure is suitable for a long tape because each section depends on the previous one.

Render

./matemium.sh render em_waves -q preview

View the complete project source.