A metal sample, with a length L, a width W, and a thickness d, is in a uniform magnetic field B = B2. The electron densi

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A Metal Sample With A Length L A Width W And A Thickness D Is In A Uniform Magnetic Field B B2 The Electron Densi 1 (59.41 KiB) Viewed 18 times

A metal sample, with a length L, a width W, and a thickness d, is in a uniform magnetic field B = B2. The electron density is n. A current / flows through it. The electrons can be regarded as moving at an average drift velocity v = vý. The current is expressed as I = ynv Wd, where q is the elementary charge, taken as a positive value. Since I nv, any electrical measurement alone cannot independently determine n and v. (1) A voltage, called the Hall voltage V, is measured between the two sides of the sample, as shown in the figure. Express Vr in terms of v, B and sample dimensions. Assuming positive values for B and I, determine the polarity of V (label the two terminal with + and signs in the figure), with the directions of B and I shown in the figure. (2) Show how to determine n from this experiment (i.c., develop an expression of n in terms of the measured quantity Vu and known parameters 1, B and sample dimensions). Vio 2 (3) For simplicity, consider the Hall detector material as a perfect conductor, i.e., there is no voltage drop along the y axis when B = 0. The Hall voltage Vis measured by a non-ideal voltmeter with a finite input impedance Rin. What is the power consumed by the voltmeter? Again, express your result in terms of I, B, sample dimensions, and n. (4) (Optional, for bonus points) Does the magnetic field do any work to provide the power consumed by the voltmeter? If not, what provides the power? Explain your answer.