Answer to Question #197147 in Electricity and Magnetism for cayyy

Question

Test instrument to measure magnetic field strengths are often based on the Hall Effect. In one instrument the “probe” is a 1.0-mm- thick, 6.0-mm - wide semiconductor with a charge-carrier density of 2.1x 1021 m^-3 , much less than the charge-carrier density in a conductor.

Passing a 60 mA current through the probe generates a Hall voltage of 120 mV. What is the magnetic field strength?

Answer 1

The Hall voltage is given by

$V_H=\frac{IB}{ned}$

where $I$ is current,

$B$ is magnetic field,

$n$ is charge-carrier density,

$e$ is charge of electron,

$d$ is thickness of the "probe"

Then:

$B=\frac{V_Hned}{I}=\frac{120\cdot2.1\cdot10^{21}\cdot1.6\cdot10^{-19}\cdot10^{-3}}{60}=0.672\ T$