Wave and Field Explorer | Physics Library

E(r, t): vectors at fixed positions

Negative ψPositive ψProbe AProbe BCoordinates: r/λ · field arrows: 0.04λ per V/m

t/T

f λ T t

Snapshot across space

One instant

ψ(s n̂, t) · signed scalar coefficient · V/m

History at fixed probes

Probe AProbe B

Local field measurements

Ideal point samples, not antenna voltages

Probe A

r/λ
r (m)
Signed ψ (V/m)
E (V/m)
|E| (V/m)

Probe B

r/λ
r (m)
Signed ψ (V/m)
E (V/m)
|E| (V/m)

ψ(r, t) = E₀ cos(k n̂·r − ωt + φ₀)
E(r, t) = ê ψ(r, t) · ê·n̂ = 0

Wave

Wave parameters

Amplitude E₀

Frequency (MHz)

Initial phase φ₀

Propagation & field direction

Propagation tilt from +z

Propagation azimuth

Transverse field rotation

Propagation n̂
Field basis ê

Probe A · coordinates / λ

x / λ

y / λ

z / λ

Probe B spacing along n̂ / λ

Field representation

Constant-phase wavefronts

Model & Julia source

Illustrative monochromatic, linearly polarized transverse plane wave in vacuum. The signed scalar ψ multiplies a transverse unit vector to give E. Negative ψ reverses E; |E| is always nonnegative. Magnetic fields and antenna responses are outside this EM01 model.

Sampling positions stay fixed while the phase pattern advances. Field arrows are values at those positions, not material objects or particle paths. Wavefront sheets have equal phase; contours have equal scalar value.

Space is displayed in wavelengths and time in periods. Changing frequency rescales the physical metres and seconds associated with these normalized coordinates. The display clock is slowed; it does not run at RF speed. Probe B is displaced from A along propagation, so its history is delayed by d/c = (d/λ)T. A monochromatic phase difference is periodic and cannot determine an unambiguous travel time without extra information.

Propagation uses polar angle θ from +z and azimuth ϕ from +x toward +y. The transverse basis is e_θ cos β + e_ϕ sin β. Camera inspection never changes the physical wave.

No source, antenna radiation pattern, modulation, finite-aperture response, medium dispersion or power calculation. The GPS preset supplies only the L1 carrier frequency, not a satellite signal simulation.

Julia source · Reference fields
Offline project · Provenance
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