In a Hall-type experiment a current of (4.302x10A-1) A is sent through the lengt

Question

In a Hall-type experiment a current of (4.302x10A-1) A is sent through the length of a metal strip having thickness (3.385x10A-4) m and width (4.61x10A-3) m. The Hall voltage across the width is measured to be (2.314x10A-4) V when a magnetic field of (3.713x10A-1) T is used What is the number of charge carries per unit volume (assuming the charge carriers possess a charge of q-e? Provide your answer in (charge carriers)/m3. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer x10

Explanation / Answer

We know that, The hall electric field has magnitude of:

Eh = Vh/d

from the defination of drift speed

vd = Eh/B = Vh/Bd

vd = 2.314 x 10^-4/(3.713 x 10^-1 x 4.61 x 10^-3) = 0.14 m/s

We know that

vd = I/A ne

n = I/A vd e

n = 4.302 x 10^-1/(3.385 x 10^-4 x 4.61 x 10^-3 x 0.14 x 1.6 x 10^-19) = 1.23 x 10^25

Hence, n = 1.23 x 10^25 /m^3

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