The constant k in Coulomb’s law depends upon

A. nature of medium

B. system of units

C. intensity of charge

D. Both (a) and (b)

Coulomb's law describes the force between two charged objects, and the constant \( k \) plays a crucial role in this relationship. To answer your question, the correct choice is D: Both (a) and (b). Let's break down why this is the case.

Understanding Coulomb's Law

Coulomb's law states that the electric 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. Mathematically, it is expressed as:

F = k * (|q1 * q2| / r²)

The Role of the Constant k

The constant \( k \) is known as Coulomb's constant, and its value depends on two main factors:

• Nature of the Medium: The medium between the charges affects the electric force. For example, in a vacuum, \( k \) has a value of approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \). However, if the charges are placed in a different medium, such as water or air, the effective force changes due to the medium's dielectric properties. This results in a modified constant, often represented as \( k' \), which accounts for the medium's permittivity.
• System of Units: The value of \( k \) also varies depending on the unit system used. In the SI system, \( k \) is expressed as \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \). In other systems, such as the Gaussian system, the constant may take on different forms or values. This highlights how the choice of units can influence the numerical representation of physical constants.

Why Not Option C?

While the intensity of charge (option C) does affect the force between the charges, it does not influence the value of the constant \( k \) itself. Instead, \( k \) remains a fixed value that serves as a proportionality constant in the equation, regardless of the magnitudes of the charges involved.

Putting It All Together

In summary, the constant \( k \) in Coulomb's law is influenced by both the nature of the medium in which the charges are placed and the system of units being used. Therefore, the correct answer is D: Both (a) and (b). Understanding these factors is essential for accurately applying Coulomb's law in various physical scenarios.