How can we explain the reason for why EM induced noise increases with the cable or wire length in analog voltage transmission?
My way of thinking is that same current is induced on the wire regardless of its length, but because the longer cable has longer resistance it causes more voltage noise. Is that correct? If not how can this be explained illustratively?
EDIT:
If the reason is the larger area hence d(A*B)/dt; then why people need to use diff ended inputs since they can zero the area by twisted wires?
Answer
My way of thinking is that same current is induced on the wire regardless of its length
It's a mistake to say that current is induced - a voltage is induced (as per Faraday's Law) and the longer the wire the more that induced voltage is. If the wire is terminated in a load this then gives rise to the current you mentioned in your question BUT that current is due to induced voltage and load.
Regards the use of twisted pair - magnetically induced interference on one wire is the same magnitude and polarity as the other wire. Electrically induced voltage is also the same so, if you use a differential amplifier it will subtract the common interference leaving just the signal (theoretically). Line impedances also need to balance for this to happen optimally.
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