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Calculating the magnetic field from the Hall Voltage

  1. Mar 16, 2010 #1
    1. The problem statement, all variables and given/known data

    You have built a sensor to detect the strength of unknown magnetic fields. You
    use a rectangular sample of copper that is 14.2 cm wide and 0.5 cm thick. You apply a
    current of 2.4 A to the copper. You know that there is a magnetic field perpendicular
    to the current because you measure a Hall Voltage of 0.1μV. What was the magnitude
    of the magnetic field that you detected?

    Assume that one electron per atom is available for conduction. (2) Copper has a
    density of 8.93 g/cm3 and a molar mass of 63.55 g/mol. (3) Remember that 1 mol of any
    substance contains 6.02 x1023 atoms (Avogadro’s number).

    2. Relevant equations

    q vd B = q EH

    VH = EH d = vd B d

    n = [tex]\frac{\rho N_{A}}{M}[/tex]

    B = [tex]\frac{E_{H}}{v_{d}}[/tex]

    EH = [tex]\frac{V_{H}}{d}[/tex]

    3. The attempt at a solution

    B = [tex]\frac{E_{H}}{v_{d}}[/tex]

    EH = [tex]\frac{V_{H}}{d}[/tex]

    Therefore B = [tex]\frac{V_{H}}{v_{d} d}[/tex] ...

    If vd = [tex]\frac{I}{n q A}[/tex] ...

    Then B = [tex]\frac{n q A V_{H}}{I d}[/tex]

    If n = [tex]\frac{\rho N_{A}}{M}[/tex]

    Then B = [tex]\frac{\rho N_{A} q A V_{H}}{M I d}[/tex]

    I worked out the following numbers (I don't know whether my error lies here or not)...

    [tex]\rho[/tex] = 8.93 x 10-9 kgm-3
    NA = 6.02 x 1023 atoms
    q = 1.602 x 10-19 C
    A = 14.2 x 10-2 x 0.5 x 10-2 = 7.1 x 10-4m2
    VH = 0.1 x 10-6 v
    M = 63.55 x 10-3 kgmol-1
    I = 2.4 A
    d = 0.5 x 10-2 m

    I have been stuck on this question for several hours now, and can't see where I'm going wrong. The answer I'm getting is 8.018 x 10-11T, when the answer expected is between 2 and 4 T apparently. Any help would be much appreciated :)
  2. jcsd
  3. Mar 16, 2010 #2


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    Science Advisor
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    Gold Member

    Check your conversions. Do you really believe that a cube of solid copper one meter on the side has a mass of 8.93 micrograms? :rolleyes:
  4. Mar 17, 2010 #3
    i've completed the question now, thanks for your help :) it was like you said, my conversion was completely wrong! also i was using the wrong measurement for d, it was in fact " 12.2 x 10-2 and not 0.5 x 10-2
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