Explain hall affect and derive the mathematical expression for hall coefficient, also describe its applications.
Sol. Hall effect
If a metal or semiconductor material carrying current I is placed under a transverse magnetic field B, then an electric field E is developed in the direction perpendicular to both I and B. this phenomenon is called as Hall Effect and is shown in Fig. Assuming that current knows from left to right in x direction and the semiconductor bar is kept under influence of magnetic field B acting in z direction, then bar will experience an electromagnetic force acting in downward direction. In the above fig. if the semiconductor bar is of p type then charge carriers are holes and current I flowing in the bar will be due to movement of holes from left to right. Since the electromagnetic force is acting downward, charge carries are pressed downwards and more holes accumulate near side I. Thus side I become more positively charged with respect to side 2. Therefore a potential difference is developed between side 1 and side. This voltage is called as hall voltage and is denoted as VH. If the semiconductor bar is n type, then current will flow in the given direction because of movement of electrons in opposite direction. Due to force, these charge carriers will accumulate downward near side 1 making it negatively charge with respect to side 2. Hall voltage developed this time is opposite to that of in case of p type semiconductor bar.