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Suppose we have a row of $5$ electromagnets, with a copper wire connecting them. Is it possible to create magnetic field in the $4^{th}$ magnet without affecting the $1^{st}$,$2^{nd}$,$3^{rd}$ and $5^{th}$ magnet by passing electric current through the copper wire. Any suggestions will be appreciated.

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If the cores are connected in sequence through a single copper wire, the desired effect will not be possible to create with standard electromagnets. By Lenz' law and the constitutional electromagnetic equations, a current will induce a field around the magnet. The most simplest of ways is to use a copper wire for each magnet individually, but this will break the serial structure that you propose.

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