Coulomb

Definition and Units

The coulomb (symbol: C) is the International System of Units (SI) derived unit of electric charge. It is named after the French physicist Charles-Augustin de Coulomb, who is known for his work on electrostatics and the formulation of Coulomb's law. One coulomb is defined as the amount of charge transported by a constant current of one ampere in one second. Mathematically, this is expressed as:

\[ 1 \, \text{C} = 1 \, \text{A} \cdot 1 \, \text{s} \]

Historical Background

Charles-Augustin de Coulomb (1736-1806) made significant contributions to the understanding of electric charge and its interactions. His experiments led to the formulation of Coulomb's law in 1785, which describes the force between two point charges. This law laid the foundation for the concept of the coulomb as a unit of electric charge.

Coulomb's Law

Coulomb's law states that the force (\( F \)) between two point charges (\( q_1 \) and \( q_2 \)) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance (\( r \)) between them. The law is mathematically expressed as:

\[ F = k_e \frac{|q_1 q_2|}{r^2} \]

where \( k_e \) is Coulomb's constant, approximately equal to \( 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2} \).

Practical Applications

Coulombs are used in various fields of science and engineering, particularly in electromagnetism, electronics, and electrochemistry. Some practical applications include:

**Capacitance**: The ability of a system to store charge is measured in farads (F), where one farad is equal to one coulomb per volt (C/V).
**Electrolysis**: The process of using electric current to drive a non-spontaneous chemical reaction. The amount of substance deposited or dissolved during electrolysis is directly proportional to the number of coulombs passed through the electrolyte.
**Battery Capacity**: The capacity of a battery is often measured in ampere-hours (Ah), which can be converted to coulombs (1 Ah = 3600 C).

Measurement Techniques

The measurement of electric charge in coulombs can be performed using various instruments and techniques, including:

**Electrometers**: Devices that measure electric charge with high precision.
**Faraday Cups**: Instruments used to measure ion currents in particle accelerators and mass spectrometers.
**Coulombmeters**: Specialized devices designed to measure the quantity of electric charge.

Quantum and Subatomic Considerations

At the quantum level, the elementary charge (e) is the smallest unit of electric charge, approximately equal to \( 1.602 \times 10^{-19} \) coulombs. This fundamental constant is crucial in the study of quantum mechanics and particle physics. The charge of an electron is \(-e\), while the charge of a proton is \(+e\).

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References

Tipler, Paul A., and Gene Mosca. "Physics for Scientists and Engineers." W.H. Freeman and Company, 2008.
Griffiths, David J. "Introduction to Electrodynamics." Pearson, 2017.