Supposing the copper strip is 17 cm long, we can also measure the ohmic voltage

Question

Supposing the copper strip is 17 cm long, we can also measure the ohmic voltage drop across the strip along the direction of the current flow. This potential difference is typically much larger than the Hall voltage. What value of B will make the Hall voltage equal to 10% of the voltage drop along the length of the copper strip?

A rectangular copper strip 1.5 cm wide and 0.10 cm thick carries a current of 5.0 A. Find the Hall voltage for a 1.2-T magnetic field applied in a direction perpendicular to the strip.

Explanation / Answer

Hall voltage, Vh = IB/nqt

Ohmic Voltage drop, Vo = rl/A

where r =resistivity of copper = 1.68*10^-8 ohm.m

l = length of the strip = 17 cm = 0.17 m

Area of cross section = 1.5*0.1 = 0.15 cm^2 = 0.15*10^-4 m2 = 1.5*10^-5 m2

So, Vo = 1.68*10^-8*(0.17)/(1.5*10^3)

But as per the question,

Vo*10/100 = Vh

So, (1.68*10^-8*(0.17)/(1.5*10^-5))*(10/100) = 5*(B)/(8.46*10^28*1.6*10^-19*0.0010)

So, B = 257.7 T <--------------------------answer

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