HALL EFFECT

                 HALL  EFFECT

Hall effect, named after its discoverer Edwin Herbert Hall (U.S Physicist) in 1879, is a conduction phenomenon which is defined as the development of a transverse electric field in a solid conducting material when it is placed under the influence of mutually perpendicular electric and magnetic fields.

                             Hall effect is observed a the result of force due to magnetic field in a moving electric charge carrier. No matter we consider current as the movement of electrons, holes or as a combination of both ( in the case of semi conductors) a perpendicular magnetic field displaces the moving electric charge in the same direction side ways at right angles to it.

Thus, the accumulation of a specific polarity in one side results in the development of a measureable potential difference within the conductor which is indicated as positive or negative by the detector.

                               Besides solids Hall effect is observed in plasma ( ionised gases) also, but it is significantly different from what we observe in solids.

Then,

Fnet = q (E + v x B )

The net force experienced by a hole moving along y- direction is the sum of forces due to electric field and Magnetic field along y- direction

Force due to electric field     = qEy  

Force due to magnetic field  = q x y- component of v x B

                                                  = q [ - vx Bz - Bz vz]

                                                  = q [ -vx Bz] ( since vz = 0 )

               

               Fnet = Fy = q( Ey – vxBz)

In order to maintain steady state condition, Ey must balance the product vx Bz. Then, Fnet = 0. This condition occurs when the holes are shifted slightly in the negative y direction due to B. As the forces are now balanced, the lateral force becomes zero as they drift along the bar.

This establishment of Ey is known as Hall effect and the resulting voltage is known as Hall voltage Vhall = Ey w

Drift velocity           Vx= Jx  / q po

So, Ey= Jx Bz /q po= RH  Jx  Bz

Po = JxBz/qEy

     =  (Ix/wt  )Bz /  q (v/w   )