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Let Fig. E27.49 represent a strip of an unknown metal of the same dimensions as those of the silver ribbon in Exercise 27.49. When the magnetic field is 2.29 T and the current is 78.0 A, the Hall emf is found to be 131 µV. What does the simplified model of the Hall effect presented in Section 27.9 give for the density of free electrons in the unknown metal?

Short Answer

Expert verified

Free electrons per cubic metern=3.7×1028m3

Step by step solution

01

Drift velocity

The drift velocity is given by

vd=Jxn|q|

02

Determine the drift velocity

The drift velocity is

vd=Jxn|q|

Jx=IA=Iy1z1vd=In|q|y1z1

Magnetic force is equal to the electric force

|q|Ez=|q|vdByvd=EzBy

Form these equations we find that

n=IByy1|q|E=(78.0A)(2.29T)(2.3×104m)(1.6×1019C)(1.31×104V)=3.7×1028m3

Therefore, simplified model of hall effect electrons per cubic meter is

n=3.7×1028m3

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Most popular questions from this chapter

An electron moves at 1.40×106m/sthrough a regionin which there is a magnetic field of unspecified direction and magnitude 7.40×10-2T. (a) What are the largest and smallest possible magnitudes of the acceleration of the electron due to the magnetic field? (b) If the actual acceleration of the electron is one-fourth of the largest magnitude in part (a), what is the angle
between the electron velocity and the magnetic field?

When a resistor with resistance Ris connected to a 1.50-V flashlight battery, the resistor consumes 0.0625 W of electrical power. (Throughout, assume that each battery has negligible internal resistance.) (a) What power does the resistor consume if it is connected to a 12.6-V car battery? Assume that Rremains constant when the power consumption changes. (b) The resistor is connected to a battery and consumes 5.00 W. What is the voltage of this battery?

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