A Hall-effect probe operates with a 120 -mA current. When the probe is placed in a uniform magnetic field of magnitude 0.0900 T, it produces a Hall voltage of 0.640 µV. (a) When it is used to measure an unknown magnetic field, the Hall voltage is 0.300 pv. What is the magnitude of the unknown field? mT (b) The thickness of the probe in the direction of B is 1.40 mm. Find the density of the charge carriers, each of which has charge of magnitude e). m-3

A Hall-effect probe operates with a 120 -mA current. When the probe is placed in a uniform magnetic field of magnitude 0.0900 T, it produces a Hall voltage of 0.640 µV. (a) When it is used to measure an unknown magnetic field, the Hall voltage is 0.300 pv. What is the magnitude of the unknown field? mT (b) The thickness of the probe in the direction of B is 1.40 mm. Find the density of the charge carriers, each of which has charge of magnitude e). m-3

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Magnetic Fields

Section: Chapter Questions

Problem 36P: A Hall-effect probe operates with a 120-mA current. When the probe is placed in a uniform magnetic...

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The Hall effect finds important application in the electronics industry. It is used to find the sign and density of the carriers of electric current in semiconductor chips. The arrangement is shown in Figure P22.66. A semiconducting block of thickness t and width d carries a current I in the x direction. A uniform magnetic field B is applied in the y direction. If the charge carriers are positive, the magnetic force deflects them in the z direction. Positive charge accumulates on the top surface of the sample and negative charge on the bottom surface, creating a downward electric field. In equilibrium, the downward electric force on the charge carriers balances the upward magnetic force and the carriers move through the sample without deflection. The Hall voltage ΔVH = Vc − Va between the top and bottom surfaces is measured, and the density of the charge carriers can be calculated from it. (a) Demonstrate that if the charge carriers are negative the Hall voltage will be negative. Hence, the Hall effect reveals the sign of the charge carriers, so the sample can be classified as p-type (with positive majority charge carriers) or n-type (with negative). (b) Determine the number of charge carriers per unit volume n in terms of I, t, B, ΔVH, and the magnitude q of the carrier charge. Figure P22.66
Check Your Understanding Repeat the previous problem with the magnetic field in the x-direction rather than in the z-direction. Check your answers with RHR-1.
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