Changing magnetic field creates potential difference

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Strafespar
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I can understand Faraday's law when viewed in this situation:

A loop moves into an area of constant magnetic field. I understand this because in terms of the Lorentz force it works and creates the same answer using magnetic flux/faraday's law. Now consider the example of the loop of wire inside an inductor with constant magnetic field throughout the inside. When the current is changed with time this creates a potential difference as well in the loop. I can't understand this in terms of the Lorentz force and thus special relativity. I have searched the forums and online but can't find an adequate solution.

Thanks in advance.
 
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The changing currents create a changing magnetic field which, by Faraday's law of induction, induces an electric Field.