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EM wave equation
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Derived from Maxwell's equations.
∇²E = μ₀ε₀ ∂²E/∂t²Maxwell's equations imply ∇²E = μ₀ε₀ ∂²E/∂t², a wave equation with speed 1/√(μ₀ε₀), matching the measured speed of light and revealing that light is electromagnetic.
This discovery united optics with electromagnetism.
Works for B as well.
In more detail
The electromagnetic wave equation for the electric field, ∂²E/∂t² = c² ∂²E/∂x², has travelling wave solutions that propagate at c. The same equation applies to the magnetic field.
Real-world uses
- Engineers use the wave equation to design antennas and waveguides.
- It explains the propagation of light in optical systems.
- Physicists derive the wave equation for light from Maxwell's equations, which shows that light is an electromagnetic wave.
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Frequently asked questions
Where does it come from?
From combining Maxwell's equations for changing fields.
Are all solutions waves?
Travelling sinusoidal solutions represent waves, and the general solution includes superpositions.
Does the wave equation predict the speed?
Yes. The coefficient in the equation gives the speed as one over the square root of mu zero epsilon zero.
Related topics in AC Circuits & EM Waves
EM wave generation · EM wave properties · Speed of light · Relation between E and B · Energy of EM waves · Poynting vector