Statcoulomb

Statcoulomb (statC or esu from electrostatic unit) is the unit of electric charge in the centimeter-gram-second (CGS) system of units. It is also known as the Franklin (Fr) after Benjamin Franklin, a pioneer in the study of electricity. The statcoulomb is defined as the charge that, when placed 1 centimeter apart in a vacuum, would repel an equal charge with a force of 1 dyne. This unit is part of the electrostatic system of units (esu) within the broader CGS system.

Definition

The statcoulomb is defined based on Coulomb's law in the CGS system. According to this law, the force (F) between two point charges (q₁ and q₂) separated by a distance (r) in vacuum is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. In the CGS system, when F is measured in dynes, r in centimeters, and the charges in statcoulombs, the constant of proportionality is set to 1, simplifying the equation to:

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

This definition implies that one statcoulomb is the magnitude of charge that, when placed 1 cm away from an equal charge in a vacuum, would produce a force of 1 dyne between the charges.

Relation to Other Units

The statcoulomb is related to the Coulomb, the SI unit of charge, through the relationship:

\[ 1 \, \text{statC} \approx 3.33564 \times 10^{-10} \, \text{C} \]

This conversion factor arises from the differences between the CGS and SI systems, particularly in the definitions of the units of charge.

Usage

The statcoulomb is primarily used in theoretical physics and electrostatics, especially in contexts where the CGS system is preferred for its simplicity in the formulation of the laws of electromagnetism. However, the SI system and the Coulomb are more commonly used in practical applications and engineering due to their global standardization.

Historical Context

The concept of the statcoulomb dates back to the 19th century when the CGS system was developed. The unit was named after Benjamin Franklin, one of the first scientists to study electricity systematically. The use of the statcoulomb has declined in favor of the SI system, but it remains an important part of the history of electrical measurement.

See Also

• Coulomb's law
• Coulomb (unit)
• Centimeter-gram-second system of units
• Electromagnetism
• Benjamin Franklin

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