A thin metal film of length 3.00 cm, width of 0.750 cm, and thickness of 24.0 mi

Question

A thin metal film of length 3.00 cm, width of 0.750 cm, and thickness of 24.0 micrometers is used to measure the Hall effect. A current of 1.80 A is maintained along the length of the sample. The Hall voltage of 22.4 microVolts is detected across its width, when a magnetic field of 2.00 Tesla is applied normal to the film. Calculate the drift velocity charge carriers. _______ Tries 0/8 Assuming the charge carriers are electrons, calculate their density. ______ Tries 0/8 By measuring the voltage drop along the sample, the resistivity of the metal was found to be 2.20 middot 10^-8 Ohm-m. Find the ratio of the Hall electric field to the electric field responsible for maintaining the electric current through the sample. _______ Tries 0/8

Explanation / Answer

qE = q (v x B)

V/d = v B

(22.4 x 10^-6) / (0.750 x 10^-2) = Vd (2)

Vd = 1.49 x 10^-3 m/s .........Ans

Vd = j / n q

1.49 x 10^-3 = ( 1.80 / (0.750 x 10^-2 x 24 x 10^-6)) / (n x 1.6 x 10^-19)

n = 4.19 x 10^28 electrons / m^3 ........Ans

Hall electric field = V/d = (22.4 x 10^-6) / (0.750 x 10^-2)

= 2.987 x 10^-3 V/m

applied electric field = I R / L

R = rho L / A = 2.20 x 10^-8 x 0.03 / (0.75 x 10^-2 x 24 x 10^-6)

= 3.67 x 10^-3 ohm

E = (1.80 x 3.67 x 10^-3) / (0.03) = 0.22 V/m

ratio = 2.987 x 10^-3 / 0.22

= 0.0136

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