According to Faraday's law of electromagnetic induction: any change in the magnetic field with time induces an electric field perpendicular to the changing magnetic field:
where E is the voltage of induced current, B is the external magnetic field, A is the corss section area of the coil, N is the number of turns of the coil, is the magnetic flux, and finally the negative sign indicates that the current induced will create another magnetic field opposing to the buildup of magnetic field in the coil based on Lenz's law.
When applying the above equation to magnetic flowmeters, the number of turns N and the strength of the magnetic field B are fixed. The Faraday's law becomes
where D is the distance between the two electrodes (the length of conductor), and V is the flow velocity.
If we combine all fixed parameters N, B, and D into a single factor , we have
It is clear that the voltage developed is proportional to the flow velocity.
A prerequisite of using magnetic flowmeters is that the fluid must be conductive. The electrical conductivity of the fluid must be higher than 3 µS/cm in most cases. A lining of nonconductive material is often used to prevent the voltage from dissipating into the pipe section when it is constructed from conductive material.