100 MHz teaching snapshot
A two-wavelength span makes nodes, peaks, and the E/B phase relation visible while the sample ledger ties each plotted location to SI values.
Physics and electromagnetism
Electromagnetic Wave Graph Calculator
Graph the electric and magnetic components of an ideal monochromatic plane wave in vacuum across position at a chosen instant and phase.
Vacuum plane-wave field graph
Inspect a true transverse-field snapshot, not a decorative sine curve
This graph evaluates E_y(x,t) and B_z(x,t) for one linearly polarized vacuum plane wave. It shows a spatial snapshot and keeps electric and magnetic units distinct; it is not a spectrum, attenuation plot, pulse envelope, or antenna near-field model.
Vacuum wavelength-
Electric-field peak-
Magnetic-field peak-
Mean intensity-
Current model evidence
Field sample ledger
Use the entered frequency, amplitude, time, and phase to evaluate both transverse components at identical positions.
| Sample | Position x (m) | Electric field Ey (V/m) | Magnetic field Bz (T) | Ey/Bz ratio |
|---|
DETAILED CALCULATION PROCESS
Formula, units, default substitution, and reconciliation
1. Governing relation
E_y = E0 cos(kx - omega t + phi); B_z = (E0/c) cos(kx - omega t + phi); lambda = c/f; <S> = 0.5 c epsilon0 E0^2
A monochromatic plane wave uses one phase for both transverse fields. Frequency fixes wavelength, E0 fixes B0 through c, and the selected time translates the spatial phase without changing amplitude.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| E0 | Peak electric-field amplitude | V/m | 10 V/m |
| B0 | Peak magnetic-field amplitude | T | E0/c |
| f | Wave frequency | Hz | 100 MHz |
| lambda | Vacuum wavelength | m | c/f |
| omega | Angular frequency | rad/s | 2 pi f |
| k | Wave number | rad/m | 2 pi/lambda |
| phi, t | Phase offset and snapshot time | rad; s | 0 deg; 0 ns |
3. Unit and sign normalization
- Megahertz are multiplied by 1e6 before computing wavelength or angular frequency.
- Degrees are multiplied by pi/180 before entering the cosine.
- Nanoseconds are multiplied by 1e-9; magnetic values remain in tesla even when normalized on the canvas.
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Five steps from physical inputs to a defensible result
- Choose the monochromatic frequency whose vacuum wavelength you want to inspect.
- Enter the peak electric-field amplitude, or zero for the valid zero-field boundary.
- Set phase offset to define the field value at the origin.
- Move snapshot time to see propagation as a phase shift while keeping wavelength fixed.
- Read exact field samples in the ledger; use the canvas for pattern recognition, not precise extraction.
PHYSICS FOUNDATIONS FOR THIS MODEL
Concepts that control this specific calculation
- A graph needs a declared independent variable
- This page puts position x on the horizontal axis while holding time fixed.
- Fields are transverse
- E_y, B_z, and propagation along x are mutually perpendicular in this ideal wave.
- The components are in phase
- Their maxima and zero crossings occur at the same x and t in vacuum.
- Frequency fixes spatial period
- One wavelength is the distance over which phase advances by 2 pi at a fixed instant.
- Different units require honest scaling
- V/m and tesla differ by c, so the canvas normalizes B only for visibility and the table reports actual values.
DEEP ANALYSIS 1
Time shifts phase, not wavelength
Increasing t translates the displayed pattern in the propagation direction; it does not stretch the spatial period.
DEEP ANALYSIS 2
Mean intensity is not the instantaneous field curve
The Poynting-vector average depends on E0 squared. Negative field values indicate direction, not negative transported energy.
DEEP ANALYSIS 3
Plane-wave assumptions fail near sources
Reactive near fields, curved wavefronts, finite beams, polarization mixtures, and material boundaries require Maxwell solutions beyond this graph.
RESULT INTERPRETATION
What the current output does and does not decide
A zero electric amplitude leaves wavelength and phase coordinates defined but makes both fields and intensity zero. This is a useful wiring boundary for the graph.
If the visual E and normalized B traces do not overlap, the implementation has broken the vacuum plane-wave phase relation; the exact ledger provides the check.
REAL USE CASES
Two decisions with different boundary conditions
Phase-referenced bench comparison
A field probe record uses a known phase reference. Adjusting phi and snapshot time distinguishes a coordinate choice from a change in frequency or amplitude.
EVIDENCE AND DATA QUALITY
What to retain with the exported result
Retain the stated propagation axis, polarization convention, amplitude definition (peak versus RMS), frequency reference, time origin, phase reference, and whether vacuum propagation is a justified approximation.
LIMITS AND EXCLUSIONS
Where this physical model stops
- The wave is monochromatic, sinusoidal, linearly polarized, and planar.
- Propagation is in vacuum with no attenuation, dispersion, reflection, or boundary.
- The electric input is peak amplitude, not RMS.
- The canvas normalizes magnetic amplitude solely for visibility; the ledger retains tesla.
- Near-field antennas, pulses, broadband spectra, standing waves, and material media are outside scope.
TERMS USED HERE
Six terms that keep the calculation unambiguous
- Plane wave
- Ideal wave with constant phase across each plane normal to propagation.
- Polarization
- Orientation and evolution of the electric-field vector.
- Wave number
- Spatial angular frequency k = 2 pi/lambda.
- Angular frequency
- Temporal angular frequency omega = 2 pi f.
- Phase
- Dimensionless argument locating a point within an oscillation.
- Poynting vector
- Electromagnetic energy-flux vector E cross H.
RELIABLE SOURCES
References supporting the equation and units
FREQUENTLY ASKED QUESTIONS
Questions specific to this calculation
Is the horizontal axis time?
No. It is position at one selected time; changing time shifts the snapshot.
Why is magnetic field normalized on the graph?
B is smaller than E by c in SI units, so a shared raw vertical scale would hide it. Exact tesla values remain in the table.
Can electric amplitude be zero?
Yes. It creates the valid zero-field boundary while preserving frequency and wavelength.
Does a negative field mean negative energy?
No. It means the vector component points opposite the chosen axis; mean energy flow remains based on squared amplitude.
Can this show a standing wave?
No. A standing wave needs at least two counter-propagating components and different node behavior.
Does this model radio propagation loss?
No. Amplitude is constant with x; use a link-budget scenario for free-space spreading.
IMPORTANT BOUNDARY
Use the result as analysis, not certification
This ideal field snapshot is for physics analysis and education, not antenna certification, EMC compliance, exposure assessment, or field-probe calibration.