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Coulomb's Law Constant:
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Coulomb's constant (k) is a proportionality constant that appears in Coulomb's law of electrostatics. It relates the electrostatic force between two point charges to the product of their charges and the inverse square of the distance between them.
The calculator uses the formula:
Where:
Explanation: The constant is derived from the fundamental properties of the electromagnetic field in vacuum and has a standard value of approximately 9 × 10⁹ N·m²/C².
Details: Coulomb's constant is fundamental in electrostatics calculations, used to determine the magnitude of electrostatic forces between charged particles, which is crucial in fields ranging from atomic physics to electrical engineering.
Tips: Enter the vacuum permittivity value in farads per meter (F/m). The default value is the standard vacuum permittivity of 8.854187817 × 10⁻¹² F/m.
Q1: Why is Coulomb's constant approximately 9 × 10⁹?
A: This value results from the fundamental constants of nature, specifically the permittivity of free space, and provides the correct scaling for electrostatic forces in SI units.
Q2: Does Coulomb's constant change in different media?
A: Yes, in different dielectric materials, the effective constant becomes 1/(4πε) where ε is the permittivity of that material, which is typically greater than ε₀.
Q3: How is Coulomb's constant related to the speed of light?
A: Coulomb's constant is related to the speed of light through the formula: k = 1/(ε₀c²), where c is the speed of light in vacuum.
Q4: What are the units of Coulomb's constant?
A: The SI units are newton-meter squared per coulomb squared (N·m²/C²), which is equivalent to volt-meter per coulomb (V·m/C).
Q5: Why is 4π included in the denominator?
A: The 4π factor appears due to the spherical symmetry of the electric field around a point charge, making the constant consistent with Gauss's law.