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Hall effect















In 1879, Edwin Hall found that an e.m.f. (electro motive force) or voltage is created transversely or across a current -carrying conductor when a perpendicular magnetic field is applied. This is popularly called the Hall effect.

 What happens during hall effect?

 The Hall effect is due to the nature of the current in a conductor. Current consists of the movement of many small charge carriers, typically electrons, holes, ions.

 To understand Hall effect let us take a slab of metal carrying a current.














The flow of electrons is always in a direction so as to oppose the convectional current flow. 

 Now we will apply a magnetic field B such that B is perpendicular to the face PQRS.













When an electric field is applied perpendicular to the magnetic field, then according to the right hand rule, a force acts on each electron in the direction SR - PQ.











Thus electrons collect along the side PQ and this makes PQ more negatively charged than the side SR.

 Therefore, the charge distribution in the slab can be represented as follows:













So, a potential difference or e.m.f. opposes the electron flow. The flow terminates when the e.m.f. reaches a particular value.

 This voltage is called the Hall voltage, VH.

Magnitude of Hall Voltage-

If VH is the Hall voltage and d is the width of the slab, then the electric field strength E,

E = VH/d

Furthermore, the force directed upwards from PQ - SR F,
F = Ee.

This force is also equal to, F = Bev. Here v is the drift velocity of the electrons.

However, the drift velocity, v = I / neA. Here n is the number of electrons per unit volume and A is the cross sectional area of the slab. 

Thus, Ee = BeI/neA.

VH/d = BI/neA.

If t is the thickness of the slab, A = td

Therefore, VH = BI/ net

Important: Hall voltages for metals are very small and would be even difficult to measure. However, Hall voltages for semi conductors are considerable values.

Hall effect in semiconductors-

In semiconductors either negative or positive charges may act as charge carriers. 

However, the magnitude force on both of these charges will be downwards. This is due to the fact that when the sign of the charge changes, i.e. from positive to negative or from negative to positive, the direction of the current also changes. 

Thus we can experimentally prove whether the charge carrier in a particular experiment was due to positive charges or whether it was due to negative charges as switching over these charges would reverse the Hall voltage.


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