Coulomb Law: What Does k Mean & Why Is 4π Used?

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SUMMARY

Coulomb's Law is expressed as F = k * (q1 * q2) / r², where k is defined as 1/(4π*ε). The constant 4π is significant as it represents the surface area of a unit sphere, which is essential in the context of electromagnetism. The vacuum permittivity (ε) is intrinsically linked to the speed of light (c) through the relationship ε₀μ₀ = 1/c², where μ₀ is the magnetic constant. This formulation emphasizes the fundamental nature of these constants in electromagnetic theory, providing clarity in mathematical expressions.

PREREQUISITES
  • Understanding of Coulomb's Law and its mathematical representation.
  • Familiarity with vacuum permittivity (ε) and its role in electromagnetism.
  • Knowledge of the speed of light (c) and its relationship to electromagnetic waves.
  • Basic concepts of geometry, specifically the surface area of a sphere.
NEXT STEPS
  • Research the derivation and implications of Coulomb's Law in electrostatics.
  • Explore the relationship between vacuum permittivity (ε) and the speed of light (c) in detail.
  • Study the significance of the magnetic constant (μ₀) in electromagnetic theory.
  • Investigate the applications of 4π in various physical laws and theories.
USEFUL FOR

Students of physics, educators teaching electromagnetism, and professionals in fields related to electrical engineering and theoretical physics will benefit from this discussion.

Bern123
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What k mean in coulomb law? it's 1/(4π*ε) but why is in this form? 4π it's related to the shape of an atom?
 
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Basically "k" has been given this strange, nonintuitive shape so that deep and fundamental results in electromagnetism look cleaner on the paper

4\pi is the surface area of a unit sphere.

The "e" is the "vacuum permittivity", closely related to the speed of light in vacuum, "c", through the formula:
\epsilon_{0}\mu_{0}=\frac{1}{c^{2}},
where \mu_{0} is called the "magnetic constant". (That formula is now used as the DEFINITION of our "e")

When we look at propagation of light waves and electromagnetic waves in general, our number "e" is so closely related to it that it pops up everywhere, and therefore, Coulomb's law has been written in such a way to make that important constant explicit, rather than using a fuzzy "k".
 
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