The rate of flow of a conducting liquid can be measured with anelectromagnetic f

Question

The rate of flow of a conducting liquid can be measured with anelectromagnetic flowmeter that detects the voltage induced by themotion of the liquid in a magnetic field. Suppose that a plasticpipe of diameter 0.10 m carries beer with a speed of 1.5 m/s. Thepipe is in a transverse magnetic field (i.e., perpendicular to thepipe axis) of about 1.5× 10 2 T.

(a) Presume the beer is an ideal conductor. What voltage will beinduced between the
opposite sides of the column of liquid?

(b) Does it matter whether the conductivity of the beer isdue to mobile
positive or negative charges?

Explanation / Answer

(a)The voltage induced between the opposite sides of thecolumn of liquid is V = E * d v = (E/B) or E = v * B v = 1.5 m/s and B = 1.5 * 10-2 T d = 0.10 m (b)The conductivity is given by = (J/E) ---------(1) J is the current density and E is the electric field J = (I/A) = (I/ * (d2/4)) =(4I/ * d2) The magnetic field is B = (oI/2r) or B = (oI/ * d) or I = (B * * d/o) o = 4 * 10-7N/A2 or J = (4 * (B * * d/o)/ *d2) or J = (4B/o * d) From (1) we get = ((4B/o * d)/E) =(4B/o * d * E) S.m-1 The condctivity of the beer is due to mobile negativecharges.This is because the rate of flow of a conductingliquid is possible only due to the motion of negativecharges(electrons).The motion of electrons in the liquid describesthe current flow in the liquid.Therefore,the conductivity of thebeer is due to mobile negative charges. The condctivity of the beer is due to mobile negativecharges.This is because the rate of flow of a conductingliquid is possible only due to the motion of negativecharges(electrons).The motion of electrons in the liquid describesthe current flow in the liquid.Therefore,the conductivity of thebeer is due to mobile negative charges.

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