Hall Effect: Introduction, Theory, Principle, Principle, And Applications

Introduction:

Hall Effect was introduced by an American Physicist Edwin H.Hall in the year 1879. It is based on the measurement of the electromagnetic field. It is also named as ordinary Hall Effect. When a current-carrying conductor is perpendicular to a magnetic field, a voltage generated is measured at right angles to the current path. Where current flow is similar to that of liquid flowing in a pipe. Firstly it was applied in the classification of chemical samples. Secondly, it was applicable in the Hall Effect Sensor where it was used to measure DC fields of the magnet, where the sensor is kept stationary.

The Lorentz force is the force experienced by a magnetic charge when acted upon by an external force field, which in this case is the transverse electric current. Since the electric current has a certain polarity, the Lorentz force pushes the enclosed magnetic charge into a direction parallel to the electric current.This motion of the magnetic charge produces a magnetic field that is perpendicular to the current, and by Faraday’s law, the resultant Lorentz force produces a tangential magnetic field. Thus, the Hall effect is also referred to as the transverse Hall–Heroult effect.The Hall voltage generated in a magnetic field is called a Hall effect. In physics, a Hall voltage is a voltage generated when current flows perpendicular to a magnetic field. It is proportional to the current density, hence inversely proportional to the sample thickness (the Hall effect does not work with planar devices).

Theory:

The Hall Effect can be defined by two variables:

• The electric current through a current-carrying conductor (the input).
• The magnetic field surrounding the conductor (the input) and one observable variable the Hall voltage that develops across a Hall plate (the output).

Magnetic Field:

In the Hall Effect, an electric current passes through a current-carrying conductor. The magnetic field surrounding the conductor is inversely proportional to the radius of the conductor. The current through the conductor can be thought of as two fluxes (current flowing in opposite directions) in quadrature; the product of the fluxes gives the total flux through the conductor.If the conductor is thin and the total flux is very small, the magnetic field around the conductor is approximately uniform. This gives an approximate formula for the magnetic field, that when multiplied by a constant, produces the Hall voltage measured across the conductor.

Voltage:

When an electric current passes through a conductor, it produces an electrostatic field around the conductor due to the electrical charges of the current. The charges of the current produce a potential difference across the conductor. If the conductor is made up of one or more conductors with currents in the same direction, it is a common case that a Hall voltage develops across the conductor, and is measured as the output.

Electromagnetic Effect:

The Hall Effect is an electromagnetic phenomenon, and it can be applied to many electromagnetic devices. This is because the current-carrying conductor, the Hall plate, and the magnetic field all have an electrical charge and produce an electric field in the space surrounding them. For example, a magnet produces a magnetic field, and when a current of electrons passes through the magnetic field, the electrons change direction and produce an electric field in the surrounding space.

Electronic Effect:

When electrons pass through the conductor, the movement of electrons produces a voltage between the electrons and the conductor. This is because they are all negative, and if they were charged in a similar way to a battery, they would repel each other and form a positive space between them and the conductor. The voltage that is produced by this is proportional to the current through the conductor. This current can be obtained by measuring the Hall voltage and applying the formula.

Principle of Hall Effect:

Hall Effect is defined as the difference in voltage generated across a current-carrying conductor, is transverse to an electrical current in the conductor and an applied magnetic field perpendicular to the current.

Hall Effect = induced electric field / current density * the applied magnetic field

Hall field is defined as the field developed across the conductor, and Hall voltage is the corresponding potential difference. This principle is observed in the charges involved in the electromagnetic fields.

Hall Effect Derivation

Consider a metal with one type of charge carrier that is electrons and is a steady-state condition with no movement of charges in the y-axis direction. Following is the derivation of the Hall-effect:

(at equilibrium, force is downwards due to magnetic field which is equal to upward electric force)

Where,

• VH is Hall voltage
• EH is Hall field
• v is the drift velocity
• d is the width of the metal slab
• B is the magnetic field
• Bev is a force acting on an electron

I=

Where,

• I is an electric current
• n is no.of electrons per unit volume
• A is the cross-sectional area of the conductor

Where,

: Hall coefficient(RH)is defined as the ratio between the induced electric field and to the product of applied magnetic field and current density.

In semiconductors, RH is positive for the hole and negative for free electrons.

Where,

• E is an electric field
• v is the drift velocity
• RH is the Hall coefficient
• H is the mobility of the hole

The ratio between density (x-axis direction) and current density (y-axis direction) is known as the Hall angle, which measures the average number of radians due to collisions of the particles.

Where,

• R is Hall resistance

Hall Effect Derivation in Semiconductors:

In semiconductors, electrons and holes contribute to different concentrations and mobilities, making it difficult to explain the Hall coefficient given above. Therefore, for the simple explanation of a moderate magnetic field, the following is the Hall coefficient:

∴

Where,

• n is electron concentration
• p is hole concentration
• e is the mobility of electron
• H is the mobility of the hole
• e is an elementary charge

Applications of Hall effect:

Hall effect finds many applications.

• It is used to determine if the given material is a semiconductor or insulator.
• It is used to measure the magnetic field and is known as a magnetometer
• They find applications in position sensing as they are immune to water, mud, dust, and dirt.
• They are used in integrated circuits as Hall effect sensors.

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