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Light is made by an electric field wave and a magnetic field wave. Induction laws state that a variation in the electric field creates a magnetic field and vice versa. Therefore can it be said that the simultaneous presence of magnetic wave and electric wave in electromagnetic waves is due to induction ? Can it be said there is an repetitive self induction in the electromagnetic waves such that the electric wave induces the magnetic wave which induces back the next electric wave period ? Can it be said that such back and forth is responsible for the light trajectory ?

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yes! it is.

It is without doubt that the radiation of an antenna works in the way you described in your question.

from Wikipedia https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Felder_um_Dipol.svg/259px-Felder_um_Dipol.svg.png

But what is a radio wave? It is important to differ between radio waves and electromagnetic waves. Radio waves are pulsed EM radiations. In each pulse electrons inside the antenna rod get accelerated and this led to photon emission. All this photons together induce the magnetic filed around the rod and if this field is strong enough the magnetic field induce a electric field. For a single photon it looks like in this sketch.

enter image description here

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The answer to your question is Maxwell's equations for Electromagnetics. Of course the variation of the electric field creates a magnetic field and vice versa, but we don't use the term induction in this case.

\begin{align} \boldsymbol{\nabla} \boldsymbol{\times} \mathbf{E} & \:=\:-\:\dfrac{\partial \mathbf{B}}{\partial t} \tag{01}\\ \boldsymbol{\nabla} \boldsymbol{\times} \mathbf{B} & \:=\:\mu_{o}\mathbf{j}+\dfrac{1}{c^{2}}\dfrac{\partial \mathbf{E}}{\partial t} \tag{02}\\ \nabla \circ\mathbf{E} & \:=\: \dfrac{\rho}{\epsilon_{o}} \tag{03}\\ \nabla \circ\mathbf{B} & \:=\: 0 \tag{04} \end{align}

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