Coulomb's Constant In Calculator Converter

Coulomb's Constant (k):

\[ k = 8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2} \]

Converted Value:

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1. What is Coulomb's Constant?

Coulomb's constant (k) is a proportionality constant in Coulomb's law, which describes the electrostatic force between two charged particles. It relates the electrostatic force to the product of the charges and the inverse square of the distance between them.

2. Unit Conversion Details

The calculator converts between different unit systems:

\[ k = \frac{1}{4\pi\varepsilon_0} \approx 8.9875517873681764 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2} \]

Conversion factors:

CGS units: 1 N·m²/C² = 10⁷ dyn·cm²/statC²
Atomic units: 1 N·m²/C² ≈ 2.3071 × 10^-28 Eh·a0·e⁻²

3. Importance in Physics

Details: Coulomb's constant appears in electrostatic calculations, quantum mechanics, and electromagnetic theory. It's fundamental for understanding electric fields and forces.

4. Using the Calculator

Tips: Enter the value of Coulomb's constant (default is standard value in N·m²/C² ×10⁹) and select the desired output unit system.

5. Frequently Asked Questions (FAQ)

Q1: Why is Coulomb's constant often written as 1/4πε₀?
A: This form appears naturally in Maxwell's equations and relates to the permittivity of free space (ε₀).

Q2: What's the exact value of Coulomb's constant?
A: k = 8.9875517873681764 ×10⁹ N·m²/C² exactly, as it's now defined through the defined values of ε₀ and c.

Q3: How does this relate to the fine-structure constant?
A: The fine-structure constant α = e²/(4πε₀ħc) can be expressed using k as α = ke²/ħc.

Q4: Why are there different unit systems for this constant?
A: Different fields of physics (CGS vs SI vs atomic units) use different base units for convenience in their domains.

Q5: Does this constant change in different media?
A: In materials, the effective constant is k/εᵣ where εᵣ is the relative permittivity of the medium.