The electrostatic force between two point charges `q_(1)` and `q_(2)` at separation r is given by F=`k. (q_(1)q_(2))/(r^(2))`. The constant k

Options

A. Depends upon system of units only
B. Depends upon medium between the charges
C. Depends on both 1 and 2
D. Is independent of both 1 and 2

Answer

To solve the question regarding the properties of the constant \( k \) in the electrostatic force equation, we can follow these steps:

### Step 1: Understand the Formula
The electrostatic force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by the formula:
\[ F = k \frac{q_1 q_2}{r^2} \]
where \( k \) is the electrostatic constant.

### Step 2: Identify the Value of \( k \)
The constant \( k \) can be expressed in terms of the permittivity of free space \( \epsilon_0 \):
\[ k = \frac{1}{4 \pi \epsilon_0} \]
In SI units, the value of \( \epsilon_0 \) is approximately \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \).

### Step 3: Analyze the Dependence of \( k \)
The value of \( k \) depends on:
- The system of units being used (SI or CGS).
- The medium between the charges, as the permittivity \( \epsilon \) changes with different materials.

### Step 4: Conclusion
From the analysis, we can conclude that:
- \( k \) depends on the system of units (SI or CGS).
- \( k \) also depends on the medium between the charges (e.g., vacuum, water).

Thus, the correct option regarding the properties of \( k \) is that it depends on both the system of units and the medium.

### Final Answer
The constant \( k \) depends on both the system of units and the medium between the charges.

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