What is the value of k in the CGS system?

The value of k in the CGS (centimeter-gram-second) system refers to the Coulomb's constant, which is a fundamental constant in electromagnetism. In the CGS system, the value of k is expressed differently than in the SI (International System of Units) system. Specifically, in CGS, the value of k is defined as 1, since the units of charge are defined in such a way that the force between two unit charges is equal to 1 dyne when they are 1 centimeter apart.

Understanding Coulomb's Law in CGS

Coulomb's Law describes the electrostatic force between two point charges. In the CGS system, the law can be expressed as:

F = k * (q1 * q2) / r²

Where:

• F is the force between the charges (in dynes),
• q1 and q2 are the magnitudes of the charges (in statcoulombs),
• r is the distance between the charges (in centimeters).

Defining the Constant k

In the CGS system, the electrostatic unit of charge is the statcoulomb. When two charges of 1 statcoulomb are placed 1 centimeter apart, the force between them is defined to be 1 dyne. Therefore, the value of k is set to 1 in this context. This simplifies calculations and makes the equations more straightforward.

Comparison with SI Units

In the SI system, Coulomb's constant k is approximately equal to 8.99 x 10^9 N m²/C². This difference arises because the units of charge and force are defined differently in the two systems. In SI, the unit of charge is the coulomb, which is much larger than the statcoulomb used in CGS.

Example Calculation

To illustrate how this works, let’s say you have two charges, each of 1 statcoulomb, separated by a distance of 1 centimeter. Using Coulomb's Law in the CGS system:

F = 1 * (1 * 1) / (1)² = 1 dyne

This confirms that the force between these two charges is indeed 1 dyne, validating the definition of k as 1 in the CGS system.

Practical Implications

Understanding the value of k and how it varies between different unit systems is crucial for physicists and engineers working in fields like electromagnetism, where accurate calculations of forces between charged particles are essential. The choice of unit system can significantly affect the complexity of equations and the ease of calculations.

In summary, in the CGS system, the value of k is defined as 1, which simplifies the relationship between electric charge and force, making it easier to work with in theoretical and practical applications.