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Electricity and Magnetism

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Hall Voltage to Determine Carrier Density

EANDM-HCKGSC

A Hall voltage of $V_H = 0.35 \: \rm V$ is measured across a $W = 1 \:\rm cm$ wide strip of an unknown conductor of length $l = 2 \:\rm cm$ and thickness $d = 0.1 \:\rm cm$. The current flowing through the strip is $I = 0.6 \:\rm A$. The strip is exposed to a perpendicular magnetic field $B = 0.3 \:\rm T$. Assume the charge carriers are electrons with charge $q = 1.6 \times 10^{-19} \:\rm C$.

What is the carrier density $n$ in the unknown conductor in charges per meter cubed?

A

$-3.2 \times 10^{21} \:\rm m^{-3}$

B

$3.2 \times 10^{21} \:\rm m^{-3}$

C

$6.32 \times 10^{19} \:\rm m^{-3}$

D

$4.7 \times 10^{14} \:\rm m^{-3}$

E

$7.0 \times 10^{23} \:\rm m^{-3}$