Question

In a Hall-effect experiment, a current of 3.7 A sent lengthwise through a conductor 1.5 cm wide, 4.0 cm long, and 12 μm thick produces a transverse (across the width) Hall potential difference of 78 μV when a magnetic field of 0.76 T is passed perpendicularly through the thickness of the conductor.

a) Find the drift velocity of the charge carriers and the number density of charge carriers.
b) Show on a diagram the polarity of the Hall potential difference.

Answer 1

given,

current, I = 3.7 A

width of conductor = 1.5 cm

Length = 4 cm

thickness = 12 μm

hall potential difference = 78 μV

magnetic field = 0.76 T

a) drift velocity of the charge carrier

`v_d = (V_H)/(Bd)`

`v_d = (78 * 10^(-6))/(0.76 * 0.015)`

`v_d = 6.84 * 10^(-3)\ m/s`

number density of charge carrier

`n=(I)/(Aev_d)`

`n=(3.7)/(0.015* 12 * 10^(-6)* 1.6 * 10^(-19)* 6.84 * 10^(-3))`

n = 1.878 x 10²⁸ electrons/m³