Certainly! Let's delve into the calculation for the electrostatic constant, [tex]\( k_e \)[/tex], which is often encountered in physics, especially in the study of electric fields and forces between charged particles.
### Step-by-Step Solution:
1. Identify the Given Value:
The electrostatic constant [tex]\( k_e \)[/tex] is given as:
[tex]\[
k_e = 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2
\][/tex]
2. Understand What [tex]\( k_e \)[/tex] Represents:
The electrostatic constant, also known as Coulomb's constant, is a value used in Coulomb's Law to describe the force between two point charges. Coulomb's Law is expressed as:
[tex]\[
F = k_e \frac{q_1 q_2}{r^2}
\][/tex]
where:
- [tex]\( F \)[/tex] is the electrostatic force between the charges,
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the charges,
- [tex]\( r \)[/tex] is the distance between the centers of the two charges,
- [tex]\( k_e \)[/tex] is Coulomb's constant which scales the magnitude of the force.
3. Express the Given Constant Numerically:
The value given is already in scientific notation, which is a standard way of expressing large (or small) numbers. To interpret this more straightforwardly:
[tex]\[
k_e = 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2
\][/tex]
4. Convert the Scientific Notation to Decimal Form:
To understand the value in conventional decimal form:
[tex]\[
8.9875 \times 10^9
\][/tex]
This means that we need to move the decimal point 9 places to the right:
[tex]\[
8.9875 \times 10^9 = 8987500000.0
\][/tex]
5. Result:
Therefore, the value of the electrostatic constant [tex]\( k_e \)[/tex] is:
[tex]\[
k_e = 8987500000.0 \, \text{N} \cdot \text{m}^2 / \text{C}^2
\][/tex]
This complete, detailed interpretation and calculation illustrate the magnitude of [tex]\( k_e \)[/tex] and its significance in physical formulas related to electrostatic forces.
