Hall effect

Advertisements

Advertisements3

Advertisements4

Advertisements6

Advertisements66

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.