# Coulomb's Constant and the Speed of Light in Vacuum

1. Jun 10, 2013

### microtech

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

κkCke = 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?

2. Jun 10, 2013

### Woopydalan

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

Last edited: Jun 10, 2013