The Hall Effect

If a metal plate carrying current is placed in a magnetic field acting at right angles to the direction of the flow of the current, a voltage is developed across the plates in the direction perpendicular to both the direction of the current and that of the magnetic field. The voltage so developed is called Hall Voltage. The phenomenon is called Hall Effect.

This experiment was devised by E.H. hall to determine the sign of charge carries in a conductor. Consider a rectangular copper strip of width d and thickness h carrying the current i in the direction shown. Let a magnetic field of induction B be applied perpendicular to the direction of the current, and into the plane of the diagram. Let q be the charge carries and V_d the drift velocity of the charge carriers.

Force acting on the charges particle due to the magnetic field
        F = q (V_d x B)
If the charge carrier is Positive, it moves with a drift Velocity V_d parallel to the direction of current. If it is negative, its direction of motion is opposite to the direction of current. In both the cases, under the action of the magnetic force, the charged particle will be deflected towards right. Thus there is an accumulation of charges on the right hand side of the strip. This will set up a potential difference between the point x and y. This is called Hall potential difference V_xy.

The sign of the Hell potential difference determines the sign of the charge carries. If the carries are positive, y will be at a higher potential than x. If they are negative, y will be at a lower potential than x. Experiments have shown that in metals the charge carries are negative. This has been confirmed by the free electron model of metals as well.

For certain metals and semiconductors, the sign of the Hall potential difference seems to indicate that the charge-carriers are positive. This anomaly has been explained by the quantum mechanical band theory of solids.




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