What are the dimensions of e^2/(4*pi*epsilon_0) in terms of energy and distance?

[eku_girl83]

Here's my question:
Starting from Coulomb's law, show that e^2/(4*pi*epsilon_0) has dimensions of energy times distance.

Coulombs law is F=(1/(4*pi*episilon_0))*(q1*q2/r^2)
I understand how to convert the units for e^2/(4*pi*epsilon_0), where e is the charge of the electron, to ev * nm.
Could someone explain how I can use this in conjunction with Coulomb's law to answer the question above?

 

[Doc Al]

Start with Coulomb's law:
$$F = \frac{1}{4 \pi \epsilon_0} e^2/r^2$$
Now rearrange it to solve for $\frac{1}{4 \pi \epsilon_0} e^2$.
Does that help?

 

[eku_girl83]

When I do that, I get units of Newtons * (nanometers)^2 Is there any way that I can convert this into units of energy * distance?

 

[Doc Al]

You may be better off thinking in terms of dimensions instead of specific units.

Another hint: Energy has dimension of Force x Distance.

 

[eku_girl83]

Thanks for helping! I figured out two more dimensional analysis type problems on my own!
I guess sometimes it's easier to work with dimensions than actual units?