The Hall effect can be used to calculate the charge-carrier number density in a conductor.If a conductor carrying a current of 2.0 A is 0.5 mm thick, and the Hall effect voltage is 4.5 µV when it is in a uniform magnetic field of 1.2 T, what is the density of charge carriers in the conductor? A)1.0 x 10²⁸/m³ B)6.7 x 10²⁷/m³ C)4.6 x 10²⁷/m³ D)1.7 x 10²⁷/m³ E)1.2 x 10²⁷/m³

Question

Quizplus · Accepted Answer

The equation for calculating the charge-carrier density using the Hall effect is: 
$n=\frac{IB}{qV_Hd}$, where 
$n$ = charge-carrier number density in the conductor 
$I$ = current through the conductor (in amperes) 
$B$ = magnetic field strength (in teslas) 
$q$ = charge of the carrier (in coulombs) 
$V_H$ = Hall voltage (in volts) 
$d$ = thickness of the conductor (in meters)

Substituting the given values:

$n=\frac{(2.0A)(1.2T)}{(1.6	imes10^{-19} C)(4.5	imes10^{-6} V)(0.5	imes10^{-3}m)}\approx6.7	imes10^{27}/m^3$

Therefore, the answer is B.

The Hall Effect Can Be Used to Calculate the Charge-Carrier