# Permittivity of free space in physics

Hi,

In my physics book I have two values for the permittivity of free space:

8.854x10^-12 c^2 N^-1 m^-2

and

8.988x10^9 N m^2 C^-2

What is the difference between these two? When would I use one or the other?

Thanks.

## Answers and Replies

gneill
Mentor
Hi,

In my physics book I have two values for the permittivity of free space:

8.854x10^-12 c^2 N^-1 m^-2

and

8.988x10^9 N m^2 C^-2

What is the difference between these two? When would I use one or the other?

Thanks.

One is the permittivity of free space, εo, typically seen in Gauss' Law, while the other is 1/(4πεo), typically seen as the proportionality constant used in Coulomb's law.

Doc Al
Mentor
In my physics book I have two values for the permittivity of free space:

8.854x10^-12 c^2 N^-1 m^-2
That's the permittivity of free space, usually symbolized as ε0.

and

8.988x10^9 N m^2 C^-2
That's Coulomb's constant, usually symbolized as k. (Not the permittivity of free space!)

What is the difference between these two? When would I use one or the other?
They are related by: k = 1/4πε0.

So you can write Coulomb's law as:
F = kq1q2/r2 = 1/4πε0 (q1q2/r2)