Hall Effect Derivation

Before moving on to Hall effect derivation, students must note that Hall effect is the production of voltage difference. It is caused across an electric conductor and is transverse to this electric current. It essentially refers to the product of magnetic induction and current density when a magnetic field works perpendicular to the current flow associated with a thin film. 

Hall effect principle, on the other hand, states that the magnetic field through which current passes exerts a transverse force. This, in turn, relocates the electrical charge to a specific side of the conducting body. 

 

What are the Applications of Hall Effect? 

Understanding this concept in its initial level involves an explanation on the scope of practical application that Hall effect derivation has. These are as follows – 

  • Hall effect helps in measuring the magnetic field around an electrical charge, and thus qualifies as a magnetometer. 

  • Hall effect formula enables one to determine whether a material serves as a semiconductor or an insulator. 

  • Hall effect definition finds immense application in integrated circuits (ICs) in the form of Hall effect sensors. 

With a brief light shed on its applications, let us move on to how you can make the Hall effect derivation from scratch.

 

How to Make Hall Effect Derivation? 

Hall effect physics involves a metal body which contains a single form of charge carriers, like electrons. Also, the metal warrants a lack of movement of charges along the y-axis. 

Therefore, one has to consider the following components of Hall effect expression components to have a better understanding of the derivation – 

Abbreviations

Components

  • VH

Hall Voltage

  • EH

Hall field

  • v

Drift velocity

  • d

Metal body width

  • B

Magnetic field

  • Bev

Force acting on an electron

 

However, the I component within the Hall effect calculation stands for –nevA. In this case, ‘I’ stands for an electric current, ‘n’ signifies the number of electrons per unit volume, and ‘A’ is the conductor’s cross-sectional area. 

Therefore, the Hall effect derivation refers to the following – 

eEH = Bev \[\frac{{evH}}{d}\] = BevVH = Bvd 

However, this derivation stipulates that the force is downward facing because of the magnetic field (equal to the upward electric force), in the case of equilibrium. 

Another way to find the exact value of VH is through the following equation – 

VH = \[\frac{{ - Bi}}{{net}}\frac{{EH}}{{JB}} =  - \frac{1}{{ne}}\]

This particular equation takes the help of Hall effect coefficient derivation, which is – 

\[\frac{{EH}}{{JB}}\]

Besides, Hall coefficient (RH) implies the ratio between the product of current density and magnetic field and the induced electric field. 

However, derivation of RH takes into account the factors as stated below – 

  • E = electric field. 

  • V = drift velocity. 

  • μ = mobility of the hole. 

Therefore, RH = - \[\frac{1}{{ne}}\]μ = \[\frac{v}{E}\]= \[\frac{J}{{neE}}\] = σRH = \[\frac{{RH}}{\rho }\] (v).

Also, you should be aware of the fact that the Hall angle in Hall effect stands for the angle between electric field and drift velocity. It is essentially the ratio between density (signified by x-axis) and current density (denoted by the y-axis). 

On top of that, Hall resistance or R = \[\frac{{VH}}{i} = \frac{B}{{net}}\]

 

Try and Answer These Questions

1. Which Factor is the Hall Coefficient RH for a Conductor Independent of? 

  • The number density of charge carriers

  • Temperature 

  • Nature of the material 

  • Dimensions of the material

 

2. Which are the Charge Carriers as Per Negative Hall Coefficient? 

  • Holes 

  • Electrons 

  • Both holes and electrons 

  • None of the above 

 

3. What is the Quantity of 1/(ne) Where ‘n’ is the Number Density of Charge Carriers and ‘e’ is the Electric Charge? 

  • Peltier effect

  • Joule effect

  • Hall coefficient

  • Thomson effect 

This article is a brief explanation of the components as present in the Hall effect derivation. However, if you want to know more on this topic, stick around on this page. You can also download our Vedantu app to benefit from a personalized learning experience. 

FAQ (Frequently Asked Questions)

1. What are the components of Hall effect derivation?

The components of Hall effect derivation are Hall Voltage (VH), Hall field (EH), drift velocity (v), width of the material (d), magnetic field (B), and the force acting on an electron (Bev).

2. What is the expression of Hall coefficient?

The expression for Hall coefficient is EH/JB

3. What is a prominent application for the Hall effect?

Hall effect helps in the measurement of the magnetic field around an electric charge and differentiate a semiconductor from an insulator.