Finding mobility constant in the context of the Hall effect

In summary, a slab made of unknown material is connected to a power supply in a uniform magnetic field of 0.7 tesla. Two voltmeters are connected across the slab with a distance of 0.16 m and a steady voltage is measured. The drift speed of the mobile charges is determined to be 0.0048 m/s. The mobility of the charges is calculated to be 1.42 (m/s)/(volts/m). With a current of 0.3 ampere, there are 4.069e23 mobile charges in 1 m3 of the material. The resistance of a 0.16 m length of the slab is 2.43 ohms. The hint suggests using the
  • #1
rcyn12
1
0
A slab made of unknown material is connected to a power supply as shown in the figure. There is a uniform magnetic field of 0.7 tesla pointing upward throughout this region (perpendicular to the horizontal slab). Two voltmeters are connected to the slab and read steady voltages as shown. (Remember that a voltmeter reads a positive number if its positive lead is connected to the higher potential location.) The connections across the slab are carefully placed directly across from each other. The distance w = 0.16 m. Assume that there is only one kind of mobile charges in this material, but we don't know whether they are positive or negative.

21-107-HW_slab_sym.jpg


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
vbar.gif
of the mobile charges.
.0048 m/s (correct)
(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.)
1.42 (m/s)/(volts/m) (incorrect)
(d) The current running through the slab was measured to be 0.3 ampere. If each mobile charge is singly charged ( |q| = e), how many mobile charges are there in 1 m3 of this material?
4.069e23 carriers/m^3 (correct)
(e) What is the resistance in ohms of a 0.16 m length of this slab?
2.43 ohms (correct)

I've tried:

E=dV/h -> u=v/(dV/h) based off Drude model with dV=.00027, h=.08, v=.0048

Not sure why this wouldn't work.
 
  • #3
Did you read the hint they give at part (c)?
Which voltage drives the current through the slab?
 

1. What is the Hall effect?

The Hall effect is a physical phenomenon that occurs when an electric current is passed through a conductive material in the presence of a magnetic field, resulting in a measurable voltage perpendicular to both the current and the magnetic field.

2. How does the Hall effect relate to mobility constant?

The Hall effect can be used to determine the mobility constant of a material, which is a measure of how easily charge carriers can move through the material in the presence of an electric field.

3. Why is it important to find the mobility constant?

Knowing the mobility constant of a material is essential for understanding its electrical properties and for designing electronic devices that use the material.

4. What is the process for finding the mobility constant using the Hall effect?

The process involves measuring the Hall voltage and the applied current in a sample of the material under a known magnetic field. The mobility constant can then be calculated using the equation 𝜇 = (VH/B)(t/nI) where VH is the Hall voltage, B is the magnetic field, t is the thickness of the sample, n is the charge carrier density, and I is the applied current.

5. Are there any limitations to using the Hall effect to find the mobility constant?

Yes, the Hall effect is only applicable to materials that have a measurable charge carrier density and can be used to determine the mobility of only one type of charge carrier at a time. Additionally, the presence of impurities or defects in the material can affect the accuracy of the results.

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