A device can be used to measure the flow speed of a conducting fluid in a pipe,

Question

A device can be used to measure the flow speed of a conducting fluid in a pipe, provided that the electrical conductivity of the pipe is substantially smaller than that of the fluid. (This is the case, for example, for blood flowing through a blood vessel.) The pipe passes through a uniform magnetic field B. Voltmeter leads are placed at P and Q, in electrical contact with the fluid; the line joining P and Q is perpendicular to the magnetic flux lines. If B = 1.00E-2 T, V = 2.80E-5 V, and the diameter of the pipe is equal to d = 2.00E-3 m, find the velocity of the fluid.
Hint : The voltage change of a particle is generally the sum of works done by both electric and magnetic forces.

Explanation / Answer

potential applied = 2.8*10^-5

distance between P & Q = 2*10^-3

so E= V/d electric field

= 2.8*10^-5/2*10^-3=0.014 N/C

as fluid is moving unaffected in magnetic and electric field so net lorenz force must be zero

i.e qE + q(VxB) =0 implies V= E/B

so Velocity = 0.014/ 10^-2 = 1.4 m/s

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