Amplitude modulation transmission distortion

I need to clarify a question. Let's say that in a wire I carry a current modulated in time so that it is an amplitude modulation of a sinusoidal carrier with a modulating sinusoidal wave. In frequency domain it corresponds to the superposition of three deltas, the one for the carrier and the ones for the modulating frequency, as usual. Then this current generates a magnetic field that is picked up by another wire, and from Faraday law of induction the voltage difference induced at the ends of the wire will depends on the derivative about time of the magnetic field. So the three deltas will be derived (in other words multiplied by ) then in the end they will have an amplitude that will depend on their frequency. So the received signal will be no more an amplitude modulation like the transmitted one, the right lobe will be emphasized with respect to the left (i.e. low frequency) lobe. Therefore, with a perfect envelope detector, the reconstructed signal will be modified with respect to the one sent by this inductive link (think of it as a transformer), am I right? Thank you