ElectromagnetismIntermediate

Concept module

Electromagnetic Waves

See how changing electric and magnetic fields travel together as one rightward wave, with the local field pair, source-to-probe delay, and propagation cue all tied to the same compact live stage.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 2.57 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s2.57 s

Electromagnetic Waves

A paired field lane shows the electric field on one axis and the magnetic field on a perpendicular lane, while the probe and graphs stay tied to the same traveling pattern.

Live setup

Graphs

Switch graph views without breaking the live stage and time link.

Probe field pair

Tracks the electric field at the probe and the display-scaled magnetic field at that same point, so their shared timing stays visible.

time (s): 0 to 2.57field value: -2 to 2

E at probeB at probe (x3 display)

Hover or scrub to link the graph back to the stage.time (s) / field value

Controls

Adjust the physical parameters and watch the motion respond.

Electric amplitude

E_{0}

1.2 arb.

Changes the electric-field height and the matching magnetic-field height without changing the timing relations.

Wave speed

v

2.8 m/s

Controls how quickly the field pattern travels to the right.

Wavelength

λ

1.8 m

Controls the crest-to-crest spacing of the shared field pattern.

Probe position

x_{p}

2.7 m

Moves the live measurement point along the propagation axis.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 1

At one probe location, the electric and magnetic fields reverse together. The local delay belongs to source versus probe, not to E versus B at the same point.

Try this

Watch one probe marker through several cycles and compare the two traces on the probe-field graph.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

E_{0}

Electric-field amplitude

1.2 arb.

Changes the size of the electric oscillation and the matching magnetic oscillation without changing wavelength or delay.

Graph: Probe field pairGraph: Source and probe electric fieldOverlay: Propagation triad

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one prompt at a time. Each one points at a field-pair relation the current stage and graphs already show in the live state.

ObservationPrompt 1 of 1

Graph: Probe field pair

At one probe location, the electric and magnetic fields reverse together. The local delay belongs to source versus probe, not to E versus B at the same point.

Try this

Watch one probe marker through several cycles and compare the two traces on the probe-field graph.

Why it matters

This is the main conceptual shift from treating electric and magnetic fields as separate timelines.

Control: Probe positionGraph: Probe field pairOverlay: Propagation triad

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

3 visible

Overlay focus

Wavelength guide

Marks one full crest-to-crest spacing directly on the electric-field lane.

What to notice

Changing lambda re-spaces the electric and magnetic patterns together because they are the same traveling wave read on two perpendicular lanes.

Why it matters

It keeps wavelength spatial and visible instead of treating it as a formula-only quantity.

Control: WavelengthGraph: Probe field pairGraph: Source and probe electric fieldEquation

λ

At t = 0 s, the electromagnetic wave travels right at 2.8 m/s with wavelength 1.8 m, so the field pattern repeats at 1.56 Hz with period 0.64 s. At the probe x = 2.7 m, the electric field is 4.41e-16 arb. and the magnetic field is 1.57e-16 arb.; the probe lags the source by 1.5 cycles after 0.96 s of travel delay.

Equation detailsDeeper interpretation, notes, and worked variable context.

Electric-field wave model

The electric field oscillates in time while repeating in space with wavelength lambda.

E_{y} (x, t) = E_{0} sin (2 π (\frac{x}{λ} - f t))

E_{0}

Electric-field amplitude 1.2 arb.

λ

Wavelength 1.8 m

Local field-pair rule

In this bounded model, the magnetic field stays in phase with the electric field while its amplitude scales inversely with the wave speed.

B_{z} (x, t) = \frac{E _{y} ( x , t )}{v}

E_{0}

Electric-field amplitude 1.2 arb.

v

Wave speed 2.8 m/s

Wave relation

Wave speed connects the spacing of the pattern to the rate at which the source launches new cycles.

v = f λ

v

Wave speed 2.8 m/s

λ

Wavelength 1.8 m

Source-to-probe delay

A point farther downstream repeats the source later because the pattern still has to travel that distance.

Δ t = \frac{x _{p}}{v}

v

Wave speed 2.8 m/s

x_{p}

Probe position 2.7 m

Propagation direction

The local field directions together determine the direction the wave is traveling on this stage.

E \times B ∥ + \overset{x}{^}

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Short explanation

What the system is doing

Electromagnetic waves are the intuition-first place where changing electric and magnetic fields stop looking like separate chapters. In one traveling wave, the electric field and magnetic field oscillate together at each location while the whole pattern moves through space. The local field directions stay perpendicular, and the propagation direction belongs to the pair rather than to one field alone.

This module keeps that story compact. One shared stage shows the electric lane, the magnetic lane, a movable probe, and a local propagation triad. The same electric amplitude, wave speed, wavelength, and probe position drive the stage, both graphs, the overlays, the prediction prompts, the worked examples, and the quick test so the wave picture stays tied to one honest field pattern.

Key ideas

01At one location in this bounded model, the electric and magnetic fields are in phase. When the electric field crosses zero, the magnetic field crosses zero there too.

02Wave speed, wavelength, and frequency still obey the same traveling-wave relation as other waves: v = f lambda.

03For the same electric field pattern, a slower wave in this model has a larger magnetic amplitude because B = E / v.

04Propagation delay belongs to the distance between locations, not to a lag between E and B at the same point. A downstream probe repeats the source later by x_p / v.

Live field-pair checks

Solve the exact state on screen.

Read the local field pair and the source-to-probe timing directly from the live wave now on screen. The same stage state drives the graphs and the algebra below.

Live valuesFollowing current parameters

At the current probe and time t = 0\,\mathrm{s}, what electric and magnetic field pair belongs to the same passing wave?

E_{0}

Electric-field amplitude

1.2 arb.

v

Wave speed

2.8 m/s

λ

Wavelength

1.8 m

x_{p}

Probe position

2.7 m

1. Read the live wave timing

The current setup has

f = \frac{v}{λ} = 1.56 Hz

, so the probe sits 1.5 cycles behind the source.

2. Read the electric field at the probe

From the live snapshot, the probe electric field is

E_{p} = 4.41 e - 16 arb.

, so the electric arrow points near zero.

3. Build the matching magnetic field

Using the bounded pair rule

B = E / v

, the same probe has

B_{p} = 1.57 e - 16 arb.

, so the magnetic marker points near zero.

Current field pair

E_{p} = 4.41 e - 16 arb., B_{p} = 1.57 e - 16 arb.

The probe is near a local zero crossing, so both fields are small together rather than one lagging behind the other.

Propagation-triad checkpoint

Suppose the probe snapshot shows the electric field pointing upward, but the stage still says the wave must propagate to the right. What must the magnetic field direction be at that same point if the local field pair is still honest?

Prediction prompt

Answer from the propagation triad rather than from isolated memorization.

Check your reasoning

The magnetic field must point out of the page.

In the stage convention, an upward electric field crossed with an out-of-page magnetic field points to the right. If the magnetic direction flipped instead, the local pair would imply leftward propagation.

Common misconception

The magnetic field is a delayed after-effect of the electric field, so E should peak first and B should respond later at the same point.

In this model, E and B belong to the same passing wave pattern. At one fixed point, they rise, cross zero, and reverse together rather than taking turns.

The real delay is spatial: a probe farther downstream sees the same oscillation later because the pattern needs time to travel there. That source-to-probe lag is different from the local E/B relationship at one position.

Quick test

Reasoning

Question 1 of 4

Answer from the live field logic, not from isolated formulas. These checks ask what the wave picture must mean about pairing, propagation, and timing.

In this stage convention, the electric field at the probe points upward and the wave still propagates to the right. Which magnetic-field direction matches that local field pair?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows a rightward-traveling electromagnetic wave on a shared horizontal axis. The top lane shows the electric field, the lower lane shows the magnetic field with a display scale note, and a movable probe marks the currently sampled downstream position.

Optional overlays can label one wavelength, the source-to-probe delay, and a local propagation triad that combines the electric direction, magnetic direction, and rightward travel cue. A readout card summarizes electric amplitude, magnetic amplitude, wave speed, wavelength, frequency, probe position, and the current local field values.

Graph summary

The probe-field graph compares the electric field and display-scaled magnetic field at one probe on the same time axis so their shared timing can be read directly. The source-probe graph compares the source electric field with the downstream probe electric field, making travel delay and phase lag visible without leaving the same simulation state.

Carry the wave story forward

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Turn EM waves into lightOptics

Electromagnetic Waves

See each variable before you move it.

Wavelength guide

What the system is doing

Solve the exact state on screen.

At the current probe and time t = 0\,\mathrm{s}, what electric and magnetic field pair belongs to the same passing wave?

In this stage convention, the electric field at the probe points upward and the wave still propagates to the right. Which magnetic-field direction matches that local field pair?

Keep moving through the concept map.

Light as an Electromagnetic Wave

Polarization

Refraction / Snell's Law