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## Homework Statement

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).

## Homework 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]

## 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 :)