PHYS·06 Magnet — two opposite magnetic poles summed over more than a thousand iron-filing probes: each filing aligns with the local field vector and brightens with its strength; tap the hero to call the nearest pole to your finger, drag the poles on the bench, double-tap empty space to swap polarity

Physics Lab · Experiment 06 · magnetostatics

The invisible, combed.

Two opposite poles, summed over a thousand iron filings. Each filing is a compass needle — it samples the local field vector, turns to match it, and brightens where the field is strong. Tap anywhere and the nearest pole glides to your finger, dragging the whole invisible geometry with it.

B = B₊ + B₋ · far field ∝ 1/r³
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[00]The apparatus

the first experiment in the series with no time in it — every frame is a fresh evaluation

Field
two opposite poles, each contributing r̂/r² — their sum is a physical dipole whose far field cancels down to 1/r³
Probes
up to 1,800 filings; each takes atan2 of the local vector for its angle and |B| for its brightness and length — nothing travels from N to S
Superposition
the picture is the vector sum at every filing, recomputed from scratch every frame — drag a pole and the whole geometry follows instantly
Softening
an ε² inside r² so the 1/r² singularity at each pole can't blow up under a fingertip
Interaction
hero: tap calls the nearest pole · bench: drag either pole, double-tap empty space to swap polarity
Status
🟢 aligned · pauses offscreen · reduced-motion shows the combed field without the shimmer, and still redraws when you move a pole
[01]Six alignments

everything a dipole knows how to say

01 · direction

Nothing flows

Field lines look like traffic but they're contours of a map. Each filing is an orientation probe frozen in place — its angle is the local vector, and the "lines" you see are your eye connecting agreements between neighbours.

θ = atan2(By, Bx)
02 · magnitude

Crowding is strength

Brightness and length track |B|. That's the whole reason textbook lines bunch at the poles.

03 · superposition

Every pole votes

The displayed field is the vector sum at every probe, every frame. Drag the poles together and the votes pile up between them; pull them apart and each keeps its own little kingdom.

04 · the dipole

No monopoles sold separately

Cut a magnet in half and you get two smaller magnets — never a lone pole. The two charges here are the model, and their opposition is why the far field dies as 1/r³ instead of 1/r².

∇·B = 0
05 · softening

Taming the singularity

1/r² diverges at r = 0. A small ε² in the denominator keeps the bench stable when a pole sits directly under your finger.

06 · the compass

Earth is the third magnet

A real compass is one filing sitting in the planet's own dipole — a field so large that every needle on the bench would agree, everywhere, and call the agreement north.

[02]The bench

drag N or S · double-tap empty space = swap polarity · strength and filings drive the hero too

strength 86 filings 1300
Field note: 01 through 05 integrated equations forward in time — pendulums accumulated error, waves carried history, fire spent fuel. 06 has no time at all. The field is a pure function of two positions; every frame throws the last one away and evaluates fresh. Nothing here remembers anything, which is exactly why it feels so obedient under your finger: what shimmers is you.