Undergrad Finding mobility constant in the context of the Hall effect

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SUMMARY

The discussion focuses on calculating the mobility constant of mobile charges in a slab subjected to a magnetic field of 0.7 tesla. The drift speed of the charges was determined to be 0.0048 m/s, while the mobility was incorrectly calculated as 1.42 (m/s)/(volts/m). The current through the slab was measured at 0.3 amperes, leading to a correct calculation of mobile charge density at 4.069e23 carriers/m³ and the resistance of the slab at 2.43 ohms. Key insights include the importance of identifying the correct electric field contribution driving the current.

PREREQUISITES
  • Understanding of the Hall effect and its implications in conductive materials.
  • Familiarity with the Drude model of electrical conduction.
  • Knowledge of basic electromagnetism, including magnetic fields and forces on charges.
  • Ability to perform calculations involving drift velocity, mobility, and charge density.
NEXT STEPS
  • Study the relationship between electric field and drift velocity in conductive materials.
  • Learn about the Drude model and its application in determining charge mobility.
  • Explore the implications of the Hall effect in various materials and its practical applications.
  • Investigate methods for measuring current and voltage in experimental setups involving magnetic fields.
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism or materials science who are interested in the behavior of charges in magnetic fields and the calculation of mobility constants.

rcyn12
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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.
 
Did you read the hint they give at part (c)?
Which voltage drives the current through the slab?
 

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