Electromagnetic Waves


Wave Equation (in 1-Dim)

$$ \large \frac{\partial^2 E}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2 E}{\partial t^2} $$$$ \large \frac{\partial^2 B}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2 B}{\partial t^2} $$

Then, the solutions are

$$ \large E = E_\text{max} \cos (kx - \omega t) $$$$ \large B = B_\text{max} \cos (kx - \omega t) $$

Speed of Light

$$ \large c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} $$$$ \large c = \frac{|E|}{|B|} $$$$ \large c = \nu \lambda = \frac{\omega \lambda}{2\pi} = \frac{\omega}{k} $$

Reflection

  • No phase change in the magnetic field
  • 180° ($\pi$) phase change in the electric field

Vice versa is true when reflection occurs at lower refractive index interface.

  • GRE Physics GR0177: Problem 066

Magnitude

$$ \large |\vec{B}| = \frac{|\vec{E}|}{c} $$
  • GRE Physics GR0177: Problem 095

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