Problem 1

Consider Hall's experiment indicated in Fig. 1. The material is a metal with a density n of charge carriers each with charge q and mass m. The Hall voltage VH  is measured for a given applied field B current I and conductor thickness t. From these variables the so called Hall coefficient for the material is determined: RH =VH t / IB      (1)

(a) For positive charge carriers, indicate on a sketch the carrier drift velocity v and which side of the conductor has positive and negative Hall voltage.

(b) For negative charge carriers, indicate on a sketch the carrier drift velocity and which side of the conductor has positive and negative Hall voltage.

(c) Show that the Hall coefficient RH = 1/nq . To do this you may need the following formulae that you should derive or argue for: v = E/B, I = J w t, and      J = n q v .

(d) Calculate the Hall voltage for an experiment on a conductor where n = 3.7×10²² cm^-3, q = 1.602×10^-19 C. The current I = 100 mA, the conductor thickness t = 0.1 mm, and the magnetic field B = 0.5 Tesla.

Figure 1: Experimental setup to measure the Hall coefficient for copper