Physics · Electromagnetism

Electromagnetic Waves

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Light as an Electromagnetic WaveTurn EM waves into light

Key takeaway

At one probe, the electric and magnetic fields are a paired local reading: they cross zero and reverse together in this model.
Source-to-probe delay is about travel through space, so changing probe position or speed changes when the downstream copy appears.
The same wave speed appears in both v = f lambda for timing and B = E / v for this stage's magnetic scale, so the two effects should be named separately.

Common misconception

The magnetic field is a delayed response that peaks after the electric field at the same point.

In this model, E and B are two parts of the same passing wave. At one fixed point they rise, cross zero, and reverse together.

Continue with related wave ideas

Keep this idea moving

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Turn EM waves into lightOptics

Light as an Electromagnetic Wave

Connect electromagnetic waves to visible light, color, frequency, and the broader spectrum while one compact stage keeps the spectrum rail, field-pair sketch, and medium-linked wavelength changes tied together.

Test wave orientationOptics

Polarization

Use one compact polarizer bench to see polarization as the orientation story of transverse waves, how angle mismatch sets transmitted light, and why one ideal polarizer makes unpolarized light emerge with one chosen axis.

Carry the wave into opticsOptics

Refraction / Snell's Law

Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.

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Reference and support

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Equation snapshotMagnetic-field pair rule · Wave relationShow 3 equations

Use v = f lambda for the traveling-wave timing, then use B = E / v only as this bounded stage's local field-pair rule.

Magnetic-field pair rule
$B_{z} (x, t) = \frac{E _{y} ( x , t )}{v}$
In this bounded model, the magnetic field stays in phase with the electric field at the same point, and its amplitude scales as E / v.
Wave relation
$v = f λ$
Wave speed tells you how fast one wavelength of pattern is launched each cycle.
Source-to-probe delay
$Δ t = \frac{x _{p}}{v}$
A point farther downstream copies the source later because the wave pattern needs time to reach it.

Why it behaves this way

Explanation

Electromagnetic waves are where changing electric and magnetic fields appear as one moving pattern rather than two separate topics. At each location, the electric and magnetic fields rise, cross zero, and reverse together while the whole pattern travels through space. The field directions stay perpendicular, and the propagation direction is set by the pair rather than by either field alone.

This module keeps that picture 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 worked examples, the prediction prompts, and the quick test, so every representation refers to the same traveling wave.

Key ideas

01At one fixed location in this model, the electric and magnetic fields are in phase: when E crosses zero, B crosses zero there too.

02Wave speed, wavelength, and frequency are linked by the same traveling-wave relation as other waves: v = f \lambda.

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

04A downstream probe sees the same oscillation later by x_p / v. That delay is about source versus probe, not about E versus B at one point.

Worked examples

Work from the live wave

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

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

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Example 1 of 2

Frozen valuesUsing frozen 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. Use v and \lambda to read the current 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. Use the local field-pair rule to find the 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.

Probe 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.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

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

Optional overlays can mark 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 from the same wave state.

Graph summary

The probe-field graph compares the electric field and the 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. This makes the travel delay and phase lag visible for one wave without leaving the same simulation state.

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