Problem 24.49 Irrigation channels that require regular flow monitoring are often

Question

Problem 24.49

Irrigation channels that require regular flow monitoring are often equipped with electromagnetic flowmeters in which the magnetic field is produced by horizontal coils embedded in the bottom of the channel. A particular coil has 100 turns and a diameter of 6.0 m. When it's time for a measurement, a 5.0 A current is turned on. The large diameter of the coil means that the field in the water flowing directly above the center of the coil is approximately equal to the field in the center of the coil. The field is directed downward and the water is flowing east. The water is flowing above the center of the coil at 1.5 m/s .

Part A

What is the magnitude of the field at the center of the coil?

Part B

What is the direction of the force on a positive ion in the water above the center of the coil?

Part C

What is the magnitude of the force on an ion with a charge +e?

The force points north. The force points east. The force points south. The force points west.

Explanation / Answer

A)

Magnitude of field at center :

B = u*N*I/(2*R) = 1.26*10^-6*100*5/(6) = 1.05*10^-4 T

B)

Direction of Force is given by the vector product of magnetic field and velocity

Magnetic field is towards bottom, velocity is towards East

So, Magnetic froce is towards NORTH <-----------answer

C)

Magnitude of force = q*v*B

So, F = 1.6*10^-19*1.5*1.05*10^-4 = 2.52*10^-23 N <-----answer

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