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I know that a changing magnetic field creates an electric field, and a moving magnet near a coil will cause a current flow, but I'm wondering how this can happen if a wire and each atom in the wire is supposed to be neutral? Shouldn't neutral charges not feel any effect under an electric field?

Thanks

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I'll explain on a basic level. The specialty of conductors is that it is made of atoms with loosely held electrons.The atoms that make the conductor is neutral but since the electrons are loosely held, when an electric field is applied the electrons move.

So the total conductor as a whole is neutral, but due to the availability of free electrons ,current is generated.