Part A When a current I travels along a conducting plate of width w , which lies

Question

Part A

When a current I travels along a conducting plate of width w, which lies perpendicular to a magnetic field B, a potential difference V develops across the plate as shown in the figure below.

Show that, in equilibrium, the potential difference across the plate is given by

  V=vBw  

where v is the velocity of the charges moving in the conductor.

Part B

Suppose we wish to use the Hall effect to measure the flow of blood in an artery. If we apply a magnetic field transverse to the direction of blood flow, it will cause the positively- and negatively-charged ions in the blood to separate and result in a voltage across the artery. Assume that the artery has a square cross section of area   a2 , where a =4.0 mm is the length of each side. Assume that the velocity is the same throughout the cross section and that the applied magnetic field has a magnitude 0.50 mT. If a voltage difference of 1.0   ? V is produced, what is the magnitude of the velocity of the blood in the artery?

Part C

What is the volume flowrate of blood in the artery, expressed in units of mL/s?

Part A When a current I travels along a conducting plate of width w, which lies perpendicular to a magnetic field B, a potential difference V develops across the plate as shown in the figure below. Show that, in equilibrium, the potential difference across the plate is given by V=vBw where v is the velocity of the charges moving in the conductor. Part B Suppose we wish to use the Hall effect to measure the flow of blood in an artery. If we apply a magnetic field transverse to the direction of blood flow, it will cause the positively- and negatively-charged ions in the blood to separate and result in a voltage across the artery. Assume that the artery has a square cross section of area a2 , where a =4.0 mm is the length of each side. Assume that the velocity is the same throughout the cross section and that the applied magnetic field has a magnitude 0.50 mT. If a voltage difference of 1.0 ? V is produced, what is the magnitude of the velocity of the blood in the artery? Part C What is the volume flowrate of blood in the artery, expressed in units of mL/s?

Explanation / Answer

a) The voltage created is due to flux changing

Flux = B.dS = B*wL ( wL is area L is length of rectangle)

Emf created = -d/dt (Flux) = -d/dt*L(Bw) = B*w*v

So at equilibrium, potential difference across the plate is B*w*v (ans)

2) Voltage created = vBL = v * 0.5*10^(-3)* 4*10^(-3) = 1 *10^(-6) V

v = 0.5 m/sec (ans)

3) Volume flowrate = Av = 4*4*0.5 *1000 = 8000 mm^3/sec = 8 mL/sec (ans)

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