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I know that a constant current doesn't create induced emf, however, I do not know why a changing one does. Are there any ways to understand it briefly/easily, or is it just the way it is?

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  • $\begingroup$ Physics doesn't ever really answer "why" things are. It mostly tries to describe what we observe in the universe around us. In this case, we observe a back-emf when we try to change the current through a loop, and we can describe the effect with Faraday's Law. $\endgroup$ – The Photon Dec 22 '18 at 18:26
  • $\begingroup$ Okay, thank you! I do not want to be like memorizing equations without understanding what's really happening, but I guess I can do it without knowing the why for most cases. $\endgroup$ – Vyun Dec 22 '18 at 20:55
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You can understand this through the Faraday Law:

$$ \varepsilon = - \frac{\Delta \Phi_B}{\Delta t}$$

Here $\varepsilon$ is the EMF, $\Phi_B$ is the magnetic flux which equals the multiplication of a magnetic field $\bf B$ and the area $\bf A$ crossed by $\bf B$, whereas $t$ is time, and $\Delta$ represents changes. So the equation just says that the EMF can be produced by the magnetic flux that changes over time.

Furthermore, in the special case you mentioned $\bf B$ is produced by the electric current. So assuming there's no change in $\bf A$, the only way to produce $\varepsilon$, i.e. the EMF, is by having $\bf B$ that's changing over time, and in order to get $\bf B$ that's changing over time you need an electric current that's changing over time too. So that's how it's explained!

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