(adsbygoogle = window.adsbygoogle || []).push({}); 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 v_{d}B = q E_{H}

V_{H}= E_{H}d = v_{d}B d

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

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

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

3. The attempt at a solution

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

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

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

If v_{d}= [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}

N_{A}= 6.02 x 10^{23}atoms

q = 1.602 x 10^{-19}C

A = 14.2 x 10^{-2}x 0.5 x 10^{-2}= 7.1 x 10^{-4}m^{2}

V_{H}= 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^{-11}T, when the answer expected is between 2 and 4 T apparently. Any help would be much appreciated :)

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# Homework Help: Calculating the magnetic field from the Hall Voltage

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