Permittivity of free space in physics

[jimmy42]

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.

 

[gneill]

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, ε_o, typically seen in Gauss' Law, while the other is 1/(4πε_o), typically seen as the proportionality constant used in Coulomb's law.

 

[Doc Al]

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)