Coulomb's Constant and the Speed of Light in Vacuum

[microtech]

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

κ ≡ k_C ≡ k_e = 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?

 

[member 392791]

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