A thin metal film of length 2.00 cm, width of 0.500 cm, and thickness of 25.0 mi
ID: 1507354 • Letter: A
Question
A thin metal film of length 2.00 cm, width of 0.500 cm, and thickness of 25.0 micrometers is used to measure the Hall effect. A current of 2.70 A is maintained along the length of the sample. The Hall voltage of 28.0 microVolts is detected across its width, when a magnetic field of 1.60 Tesla is applied normal to the film.
A) Calculate the drift velocity of the charge carriers.
B) Assuming the charge carriers are electrons, calculate their density.
C) By measureing the voltage drop along the sample, the resistivity of the metal was found to be 2.60e-8 ohm-m. Find the ratio of the Hall electric field responsible for maintaining the electric current through the sample.
Explanation / Answer
A) In the equilibrium,
electric force on electron = magnetic force on electron
q*E = q*vd*B
q*vH/L = q*v*B
vd = vH/(L*B)
= 28*10^-6/(0.02*1.6)
= 8.75*10^-4 m/s
B) vd = I/(n*e*A)
n = I/(vd*e*A)
= 2.7/(8.75*10^-4*1.6*10^-19*0.005*25*10^-6)
= 1.54*10^29 /m^3
C) use ohm's law, V = I*R
V = I*rho*L/A
V/L = I*rho/A
E = I*rho/A
= 2.7*2.6*10^-8/(0.005*25*10^-6)
= 0.5616 N/c
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