Question

Define and explain the "Hall's effect" in magnetism. What important physical properties of the charge carriers were found with the help of this effect? ii) Consider a strip of copper immersed in a magnetic field B carrying a current i as shown in figure (1). Explain how the polarities are produced on opposite sides of the strip? iii) How the Hall Potential ∆VH and the Hall's Electric Field EH are measured? iv) When the equilibrium condition is reached, no further charge flow occurs. Use Lorentz force for equilibrium state, find an equation for the density “n” of the charge carriers.
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Answer 1

Hall effect is the production of a potential difference across an electrical conductor when a magnetic field is applied in a direction perpendicular to that of the flow of current. The Hall effect is basic to solid-state physics and an important diagnostic tool for the characterization of materials – particularly semi-conductors. It provides a direct determination of both the sign of the charge carriers, e.g. electron or holes (appendix A), and their density in a given sample. In 1879 E. H. Hall observed that when an electrical current passes through a sample placed in a magnetic field, a potential proportional to the current and to the magnetic field is developed across the material in a direction perpendicular to both the current and to the magnetic field [1]. This effect is known as the Hall effect, and is the basis of many practical applications and devices such as magnetic field measurements, and position and motion detectors. With the measurements he made, Hall was able to determine for the first time the sign of charge carriers in a conductor. Even today, Hall effect measurements continue to be a useful technique for characterizing the electrical transport properties of metals and semiconductors.

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