Coulomb Constant Calculator Math

Coulomb's Law Constant:

\[ k = \frac{1}{4\pi\epsilon_0} \approx 8.99 \times 10^9 \text{ N·m}^2/\text{C}^2 \]

Electrostatic Force (F):

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1. What Is Coulomb's Constant?

Coulomb's constant (k) is a proportionality factor that appears in Coulomb's law, which describes the electrostatic force between two charged particles. It is approximately equal to 8.99 × 10⁹ N·m²/C² in a vacuum.

2. How Does The Calculator Work?

The calculator uses Coulomb's law formula:

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

Where:

\( F \) — Electrostatic force (N)
\( k \) — Coulomb's constant (8.99 × 10⁹ N·m²/C²)
\( q_1, q_2 \) — Electric charges (C)
\( r \) — Distance between charges (m)

Explanation: The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

3. Importance Of Coulomb's Constant

Details: Coulomb's constant is fundamental to electromagnetism and is used to calculate the magnitude of electrostatic forces between charged particles, which is essential in fields ranging from atomic physics to electrical engineering.

4. Using The Calculator

Tips: Enter the values of both charges in coulombs and the distance between them in meters. The distance must be greater than zero. The calculator will compute the electrostatic force in newtons.

5. Frequently Asked Questions (FAQ)

Q1: Why is Coulomb's constant approximately 8.99 × 10⁹?
A: This value comes from the relationship \( k = \frac{1}{4\pi\epsilon_0} \), where ε₀ is the vacuum permittivity (approximately 8.85 × 10⁻¹² C²/N·m²).

Q2: Does Coulomb's constant change in different media?
A: Yes, in materials other than vacuum, the effective constant is \( k = \frac{1}{4\pi\epsilon} \), where ε is the permittivity of the material.

Q3: What is the direction of the electrostatic force?
A: Unlike charges attract and like charges repel. The calculator gives the magnitude only.

Q4: How accurate is this calculation?
A: It's exact for point charges in vacuum. For real-world applications, additional factors may need consideration.

Q5: What are typical charge values used with this calculator?
A: Elementary charge is about 1.6 × 10⁻¹⁹ C. Macroscopic charges are typically in microcoulombs (10⁻⁶ C) to millicoulombs (10⁻³ C).