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Just a thought experiment, if I move a magnet, the changing B will induce an E-field which is also time-variant. According to $\nabla\times H=\partial D/\partial t$ in Maxwell equation, the magnetic field is also induced by the time-variant E. And this process will continue to induce E and B field.

My questions are:

  1. Does that mean the total magnet or electric field is a sum of all the induced B and E?
  2. Why don't we consider the continued process in the questions of Electromagnetism?

(Basically, we consider the induced electromotive force but don't further consider the induced magnetic field)

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Indeed, changing magnetic field induced an electric field which in turn induces a magnetic field... which leads to the phenomenon known as electromagnetic waves. This is easy to see by using the relevant Maxwell equations together, as shown here.

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