All Problems

Electromagnetic Waves. Radiation

Problem 4.199

A standing electromagnetic wave with electric component \(\mathbf{E}=\mathbf{E}_{m} \cos k x \cdot \cos \omega t\) is sustained along the \(x\) axis in vacuum. Find the magnetic component of the wave \(\mathbf{B}(x, t) .\) Draw the approximate distribution pattern of the wave's electric and magnetic components \((\mathbf{E}\) and \(\mathbf{B})\) at the moments \(t=0\) and \(t=T / 4,\) where \(T\) is the oscillation period.

Reveal Answer
B=Bmsin⁡kx⋅sin⁡ωt, where Bm⊥Em, with Bm=Em/c\mathbf{B}=\mathbf{B}_{m} \sin k x \cdot \sin \omega t, \text { where } \mathbf{B}_{m} \perp \mathbf{E}_{m}, \text { with } B_{m}=E_{m} / c
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