Assume: The mobile charge carriers are either electrons or holes. The holes have

Question

Assume: The mobile charge carriers are either electrons or holes. The holes have the same magnitude of charge as the electrons. The number of mobile charge carriers for this particular material is n = 8.49 times 10^28 electrons/m^3. A constant magnetic field of magnitude points out of the paper. There is a steady flow of a horizontal current flowing from left to right in the r direction. The charge on the electron is 1.6021 times 10^-19 C. What is the magnitude of the electric field between the upper and lower surfaces? Answer in units of N/C.

Explanation / Answer

Let a=7cm=0.07m

b=3.1cm = 0.031m

B=1.2T

n=8.49*1028 electrons/m3

q=1.6021*10-19 C

i=7.6A

L=2.2 m

Area (A) = a.b= (0.07m)(0.031m)=0.00217 m2

For the Hall effect the magnetic force balances the electric force which means

qvdB=qE

E=vd B

we know that

i=nqvd A i,e vd = i / (nqA)

so the magnitude of the electric field is

E=(iB)/(nqA)

E=(7.6A)(1.2T) / (8.49*1028 * 1.6021*10-19 C * 0.00217m2)

E=3.089*10-7  N/C

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