Coulomb's Constant and the Speed of Light in Vacuum

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SUMMARY

Coulomb's constant (κ), defined as κ = 1/(4πε0) = 8987551787.36818 N•m²/C², is intricately linked to the speed of light in a vacuum (c). The relationship is established through the equation c = 1/√(μ0ε0), where μ0 is the magnetic permeability and ε0 is the electric permittivity. The dimensions of κ (N•m²/C²) and c (m/s) converge due to the underlying principles of electromagnetism, particularly when considering the division by ten million to align the values. This connection highlights the fundamental nature of electric and magnetic fields in light propagation.

PREREQUISITES
  • Understanding of Coulomb's Law and electric force
  • Familiarity with electromagnetic theory, specifically ε0 and μ0
  • Knowledge of dimensional analysis in physics
  • Basic grasp of the relationship between electric and magnetic fields
NEXT STEPS
  • Explore the derivation of Coulomb's constant from fundamental principles
  • Study the implications of the equation c = 1/√(μ0ε0) in electromagnetism
  • Investigate the significance of the 4π factor in electromagnetic equations
  • Learn about the role of dimensional analysis in physics problem-solving
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Physicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of the relationship between electric forces and the speed of light.

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Coulomb’s (electric force, electrostatic) constant (symbol κ (kC, ke)) is a proportionality constant, expressed as:

κ ≡ kC ≡ ke = 1/(4πε0) = 8987551787.36818 N•m2/C2 (exactly)

κ can also be derived from lightspeed squared divided by ten million (c2/107)...

Can someone please help me understand how the two (seemingly unrelated) dimensions (N•m2/C2 vs. m/s) are related, the expressions yielding the exact same value?
 
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Look at the equation for c. It has the electric field and magnetic field intrinsic to light, which is related to coulomb's constant

c = 1/√μ0εo

The μ has the 4π factor. The reason for the difference in dimensions is because you chose to divide by ten million because it gave you the right number. It cancels out the 10^-7 in the magnetic permeation constant
 
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