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 Current flowing in the semi conductor (x-direction)
B Applied Magnetic field (z-direction)
E 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.
, where is the drift velocity
Electric field Intensity due to Hall effect is
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 is
W- width of the specimen, d- height of the specimen.
From EQN(I) and From EQN(II)
up on multiplying with ‘d’ on both sides
, let Hall coefficient
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 is positive it’s a P-type semi conductor and negative means it’s N-type semi conductor.
- It is used to find out carrier concentrations ‘n’ and ‘p’ , by using either or .
- To find out mobilities and using the equation .
- 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.