Explain hall effect with hall mobility and hall angle, Electrical Engineering

Explain Hall effect.

Consider a slab of material wherein there is a current density J resulting by an applied electric field Ex in the x- direction. The electrons will drift along with an average velocity V‾x in the x direction; while a magnetic field of flux density Bz (wb/m2) is superposed upon the applied electric field in the Z direction the electrons will experience a Lorentz force perpendicular to V‾x and to Bz; the magnitude of this force will be specified by Bz (µx)e.

1737_hall effect1.png

Thus the electrons are driven towards one face in the sample resulting in an excess of electrons near one face and a deficiency of electrons near the other face. These charges will in turn create a counteracting electric field Ey in the y-direction. Ey would build up, till this is of sufficient magnitude to compensate the lorentz force exerted on the electrons because of the magnetic field we may hence write e Ey =Bz e( V‾x ). In steady state, a Hall voltage, VH, is thereby put in the y-direction specified by

VH = Ey .a =Bz (V‾x), a

The current density in the sample is specified with:

Jx = N. e (V‾x)

Here N=number of conduction electrons/m³

The current density can be computed from the total current and the cross section (a x b) of the sample.

Therefore,

Jx = I/a x b = N. e (V‾x)

I = N. e (V‾x) a x b   ....................................(1)

VH = BZ (V‾x) . a    ......................................(2)

Eliminating (V‾x) from equating (1) and (2) we get:

VH = I/(N.e.b)

= (1/N.e) ((BZ.I)/b)

The ratio + (1/N.e) = Ey/(JX.BZ) should be constant.

Another variable that is frequently used to explain the Hall Effect is the ratio of the currents JY to JX.

This is termed as the Hall angle and is denoted with θ θ = JY / JX = σ EY / JX

= σ RH BZ

= µ H BX

Here µ H is termed as the Hall mobility. The hall angle is equal to the average no. of radians traversed through a particle between collisions.

Posted Date: 5/21/2013 5:41:54 AM | Location : United States







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