A slab made of unknown material is connected to a power supply as shown in the f
ID: 2075495 • Letter: A
Question
A slab made of unknown material is connected to a power supply as shown in the figure. There is a uniform magnetic field of 0.8 tesla pointing upward throughout this region (perpendicular to the horizontal. Two are connected to the slab and read steady voltage as shown. (Remember that a voltmeter reads a positive number if its positive lead is connected to the higher potential location.) The across the slab are carefully placed directly across from each other. The distance w = 0.19 m. Assume that there is only one kind of mobile charges in this material, but we don't know whether they are negative. (a) Determine the (previously unknown) sign of the mobile charges, and state which way these charges move inside the slab. Which of the following are true? The mobile charges are negative and move out of the page. The mobile charges are positive and move out of the page. The mobile charges are positive and move into the page. The mobile charges are negative and move into the page. (b) In the steady state, the current moves straight along the bar, so the net sideways force on a moving charge must be zero. Use this fact to determine the drift speed 0 of the mobile charges. m/s (c) Knowing the drift, speed, determine the mobility u of the mobile charges. (Note that there are two contributions to the electric field in the bar. Think about which one drives the current.) (m/s)/(volts/m) (d) The current running through the slab was measured to be 0.3 ampere. If each mobile charge is singly charged (|phi| = e), how many mobile charges are there in 1 m^2 of this material? What is the resistance in ohms of a 0.19 m length of this slab?Explanation / Answer
a) positive and move out of page
b) delta V = 0.00027 V = EH W
EH = 0.00027 / 8 * 10-2 = 0.003375 V/m
Drift velocity = EH / B = 0.003375 / 0.8
= 0.00422 m/s
c) mobility = vd * w / delta V' = (0.00422 * 0.19) / (0.73)
= 1.09 * 10-3 (m/s)(N/C)
d) n = I / q A vd = (0.3) / (1.6 * 10-19 * 1.2 * 10-2 * 8 * 10-2 * 0.00422)
= 4.63* 1023 carriers/m3
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