Hall effect

When a transverse magnetic field ‘B’is applied to a specimen (of metal (or) Semi conductor) carrying a current Ian Electric field E is induced perpendicular to both I and B. This phenomenon is known as Hall effect.

The figure shows the  experimental arrangement to observe Hall effect  Now 

I \rightarrow Current flowing in the semi conductor (x-direction)

B\rightarrow Applied Magnetic field (z-direction)

E\rightarrow Induced Electric field is along y-direction perpendicular to both I and B.

Now charge carrier electron is moving under the influence of two fields both electric field(E) and Magnetic field(B). 

i.e, electron is under the influence of both E and B, E applies some force on electron similarly B.

under equilibrium F_{E} = F_{B}

qE = Bqv_{d}------EQN(I), where v_{d} is the drift velocity

Electric field Intensity due to Hall effect is E=\frac{V_{H}}{d}--------------EQN(II)

V_{H} is the Hall voltage between plates 1 and 2.

and d- is the distance between the two plates.

In an N-type Semi conductor, the current is due to electrons , plate 1 is negatively charged compared to plate 2.

The current density J related to charge density \rho is J = \rho v_{d}------------EQN(III)

J = \frac{Current}{Area}=\frac{I}{A}=\frac{I}{Wd}

W- width of the specimen, d- height of the specimen.

From EQN(I) E=Bv_{d} and From EQN(II) V_{H}=Ed

up on multiplying with ‘d’ on both sides E d = Bd v_{d}

V_{H} = Bd v_{d}

V_{H} = B d \frac{J}{\rho }    from EQN(III)

V_{H} = B\frac{I}{Wd\rho }d

V_{H} = \frac{BI}{\rho W}

V_{H} = \frac{1}{\rho } . \frac{BI}{W}, let Hall coefficient R_{H} = \frac{1}{\rho }

V_{H} = R_{H}. \frac{BI}{W} .

Uses of Hall effect (or) Applications of Hall effect:-

  • Hall effect specifies the type of semi conductor that is P-type (or) N-type.when R_{H} is positive it’s a P-type semi conductor and  R_{H}  negative means  it’s  N-type semi conductor.
  • It is used to find out carrier concentrations ‘n’ and ‘p’ , by using either \rho = nq  or \rho =pq.
  • To find out mobilities \mu _{n} and \mu _{p} using the equation \mu =\sigma R_{H}.
  • Some other applications of Hall effect are measurement of velocity, sorting,limit sensing etc.
  • used to measure a.c power and the strength of Magnetic field and also finds the angular position of static magnetic fields in a magnetic field meter.
  • used in Hall effect multiplier, which gives the output proportional to product of two input signals.


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Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.