# 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 $F_{E}&space;=&space;F_{B}$

$qE&space;=&space;Bqv_{d}------EQN(I)$, 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 $J&space;=&space;\rho&space;v_{d}------------EQN(III)$

$J&space;=&space;\frac{Current}{Area}=\frac{I}{A}=\frac{I}{Wd}$

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 $E&space;d&space;=&space;Bd&space;v_{d}$

$V_{H}&space;=&space;Bd&space;v_{d}$

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

$V_{H}&space;=&space;B\frac{I}{Wd\rho&space;}d$

$V_{H}&space;=&space;\frac{BI}{\rho&space;W}$

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

$V_{H}&space;=&space;R_{H}.&space;\frac{BI}{W}$ .

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 $\rho&space;=&space;nq$  or $\rho&space;=pq$.
• To find out mobilities $\mu&space;_{n}$ and $\mu&space;_{p}$ using the equation $\mu&space;=\sigma&space;R_{H}$.
• 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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