# Lenz law and magnetic pole

When a magnetic north(N) pole is placed close to an coil with out energy source, the coil behaves like an magnet and we find a North pole which opposes the magnet bar which was approximating onto the coil.

My question is, what conditions and mathematcal treatment assure us about the creation of the pole on the coil.

Please write if you have any confusion to get the question.

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Mathematically, we have Faraday's law $$\nabla \times E=-\frac{dB}{dt}$$ this is essentially the math that shows that there will be a current due to the changing magnetic field. Furthermore, this current gives rise to a magnetic field: $$\nabla \times B=\mu_0J+\frac{dE}{c^2dt}$$