Fields you can walk around

Physics diagrams are usually flat, and a flat diagram hides the part that matters: a field fills space. Every study here is a line drawing that behaves like a solid — orbit it, drag the sources, and the geometry recomputes from the governing equation rather than from an artist's guess.

Nothing here is animated by hand. Field lines come from integrating the field itself, orbits from stepping the equations of motion, induced EMF from differentiating a numerically computed flux.

Made by Soumya
/schrödinger's cat
A cat sealed in a box with a random quantum trigger is, on paper, alive and dead at once until someone opens it.
Schrödinger meant it as a complaint about that reading of quantum mechanics, not an endorsement — which is exactly why it works: it drags a superposition you cannot see at atomic scale up to a scene you can picture.
/keys
← →   previous / next study
/        back to this index
/controls
drag empty space — orbit the view
drag a marker — move the source
scroll — zoom
/reading the drawings
Line weight and opacity carry depth. Orange dashes run along the field direction. Hollow rings are probes you can drag.
/units
Constants are set to one, so readouts are ratios rather than laboratory values. The geometry and the scaling are the faithful parts.
/index
[1] /electric fieldfig. 01
Point charges and the lines between them
Field lines traced through Coulomb's law in 3D. Add charges of either sign and watch the topology rearrange.
E = kq/r²  ·  probe reads |E| and direction
[2] /magnetic fieldfig. 02
Current makes circles in the air
Closed loops around a straight wire, stacked at several heights. Bring a second wire in and the loops merge.
B = μ₀I/2πr  ·  flip the current direction
[3] /inductionfig. 03
A magnet at rest does nothing at all
Flux through the coil is integrated over its disk each frame; the meter shows its rate of change as you drag.
ε = −N dΦ/dt  ·  live EMF trace
[4] /lorentz forcefig. 04
A field that pushes only sideways
Aim the velocity arrow and the trajectory integrates into a helix — circular across the field, straight along it.
F = qv × B  ·  gyroradius and pitch
[5] /interferencefig. 05
Two sources, and the still lines
A live wire-mesh surface with the nodal hyperbolae drawn on the floor beneath it.
Δr = nλ  ·  probe names the condition
[6] /gravity wellsfig. 06
An orbit is a permanent fall
Place a satellite on the potential sheet, aim it, release. The readout classifies the conic you produced.
−GM/r  ·  eccentricity, energy, escape speed
[7] /circuit potentialfig. 07
Voltage is a height, current is a flow
The loop lies flat and the potential is plotted above it as a staircase that has to close on itself.
V = IR  ·  series or parallel branch
[8] /solenoidfig. 08
Many loops make one straight field
A full Biot–Savart sum over the winding, so the uniform bore is earned rather than assumed.
B ≈ μ₀nI  ·  turns, length, radius
[9] /velocity selectorfig. 09
Two forces that cancel at one speed
Crossed E and B fields sort a beam by speed. Three trajectories run; only the middle one reaches the slit.
v = E/B  ·  independent of charge and mass
[0] /refractionfig. 10
Light bends because one edge slows first
Wavefronts pivot as they cross the interface. Push the angle past critical and nothing crosses at all.
n₁sinθ₁ = n₂sinθ₂  ·  total internal reflection
[11] /fleming rulesfig. 11
Three directions, one right angle each
The left and right hand rules drawn as what they actually are: a cross product you can rotate and inspect.
F = IL × B  ·  motor and generator, one rule
[12] /motor loopfig. 12
A loop that can never stop turning
Force on each arm makes a couple. Switch the commutator off and the motor rocks itself to a halt.
τ = NIAB sinθ  ·  live torque trace
[13] /ac generatorfig. 13
Turning a coil writes a sine wave
The motor run backwards. Flux follows a cosine, so the induced EMF comes out as a sine.
ε = NBAω sinωt  ·  slip rings or commutator
[14] /transformerfig. 14
Trading volts for amps
Two windings sharing one flux path. Switch the supply to DC and the output disappears.
Vs/Vp = Ns/Np  ·  step up or step down
[15] /em wavefig. 15
Two fields taking turns
E and B at right angles and in phase. Orbit down the axis and the wave collapses to a cross.
c = 1/√(ε₀μ₀)  ·  linear polarisation
[16] /spacetime curvaturefig. 16
The funnel is not the gravity
Flamm's paraboloid, with a probe that reads the local clock rate as you drag it toward the horizon.
z = 2√(rₛ(r−rₛ))  ·  time dilation √(1−rₛ/r)
[17] /black holefig. 17
Light takes the only path there is
Null geodesics integrated in the Schwarzschild metric. Aim the beam until rays stop coming back.
capture below b = 3√3 M  ·  photon sphere
[18] /wormholefig. 18
Two sheets, joined at the throat
The Ellis embedding. Send a traveller through and watch the proper distance grow only linearly.
r = √(ℓ² + b²)  ·  no horizon, open throat
[19] /sum over pathsfig. 19
Light tries every route at once
Feynman's arrows, added end to end. Only the paths near the quickest one survive the sum; the rest curl into a circle.
sum over histories  ·  phase from travel time
orthographic projection · semi-implicit integration · every field solved from its own equation, 60 times a seconddrag anything that looks draggable