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Hall Effect Derivation
Hall effect is defined as the production of a voltage difference across an electrical conductor which is transverse to an electric current, and with respect to an applied magnetic field, it is perpendicular to the current. Edwin Hall discovered this effect in the year 1879.
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.
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
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
- 𝛍H 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
- 𝛍e is the mobility of electron
- 𝛍H is the mobility of the hole
- e is an elementary charge
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Applications of Hall effect
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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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FAQs on Important Derivations: Semiconductor Electronic: Material Devices and Simple Circuits - Physics Class 12 - NEET
| 1. What is the Hall Effect? |  |
| 2. How is the Hall Effect derived in semiconductors? | |
Ans. The Hall Effect in semiconductors can be derived by considering the motion of charge carriers (electrons or holes) in the presence of an applied magnetic field. By applying the Lorentz force equation and considering the equilibrium condition, an expression for the Hall voltage can be obtained.
| 3. What are the applications of the Hall Effect? | |
Ans. The Hall Effect has various applications in different fields. Some of the common applications include magnetic field sensing, current measurement, proximity sensing, position sensing, and speed detection. It is also used in Hall effect sensors, Hall effect thrusters, and magnetic field imaging.
| 4. What are some important derivations related to Semiconductor Electronics? | |
Ans. Some important derivations related to Semiconductor Electronics include the derivation of the current-voltage characteristics of a p-n junction diode, the derivation of the transistor current gain formula, the derivation of the expression for the energy band gap in a semiconductor, and the derivation of the Hall voltage in a semiconductor.
| 5. What are some frequently asked questions about Material Devices and Simple Circuits? | |
Ans. Some frequently asked questions about Material Devices and Simple Circuits include how to calculate resistance in a circuit, how to determine the current flowing through a circuit, how to calculate power dissipation in a resistor, how to analyze the behavior of diodes in a circuit, and how to calculate the voltage drop across a resistor using Ohm's Law.
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