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Coulomb's Constant Equation:
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Coulomb's constant (k) is a proportionality constant in Coulomb's law that relates the electrostatic force between two charged particles to their charges and the distance between them. It's a fundamental constant in electromagnetism.
The calculator uses the equation:
Where:
Explanation: The constant relates the electric force between charges to the inverse square of their distance, with the permittivity of free space determining how much resistance is encountered when forming an electric field in a vacuum.
Details: Coulomb's constant is fundamental to understanding electrostatic interactions and is used in calculations ranging from atomic physics to electrical engineering. It appears in Coulomb's law, Gauss's law, and many other fundamental equations of electromagnetism.
Tips: Enter the permittivity of free space in F/m (default value is 8.8541878128×10⁻¹² F/m). The calculator will compute Coulomb's constant in N·m²/C².
Q1: What is the exact value of Coulomb's constant?
A: Approximately 8.9875517923×10⁹ N·m²/C² in a vacuum.
Q2: Why is 4π in the denominator?
A: The 4π factor comes from the surface area of a sphere and appears because the electric field spreads out spherically from a point charge.
Q3: Does Coulomb's constant change in different media?
A: The value changes in different materials due to their relative permittivity (dielectric constant). The calculator gives the value for vacuum.
Q4: How is this related to the fine-structure constant?
A: Coulomb's constant appears in the expression for the fine-structure constant, which characterizes the strength of electromagnetic interactions.
Q5: Why is this constant important in quantum mechanics?
A: It's fundamental to calculating potential energy in atomic systems and appears in Schrödinger's equation for hydrogen-like atoms.