Question: consider this problem: Fig. 6.18 shows a system for measurement of fluid velocity that consists of a parallel-plate capacitor situated in a uniform time-invariant magnetic

consider this problem: Fig. 6.18 shows a system for measurement of fluid velocity that consists of a parallel-plate capacitor situated in a uniform time-invariant magnetic field. A liquid flows between the capacitor plates and the voltage between the plates is measured by a voltmeter. The velocity of the fluid can be considered to be uniform. The magnetic field lines are parallel to the plates. The conductivity and permeability of the liquid are a and p. o, respectively. The capacitor plate area is S and the separation between plates is d. Fringing effects in the capacitor can be neglected. The flux density of the applied magnetic field is B. The internal resistance of the voltmeter is Ry, while the resistance of the interconnecting conductors is negligible. Show that the velocity of the fluid is linearly proportional to the voltage V indicated by the voltmeter and find the proportionality constant

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