Relationship Between Energy, Force, Potential, and Field

[matangi7]

I was answering the question, "Since electric potential is always proportional to potential energy, why bother with the concept of potential at all?"
I answered that this is because Electric Potential Energy requires a test charge to calculate, Electric Potential is present without a test charge. Based on this, is it safe to say that Electric potential energy is to electric force as electric potential is to electric field?

 

[kuruman]

It is safe to say that. In fact the electric force is the negative gradient of the electric potential energy and the electric field is the negative gradient of the electric potential.

 

[matangi7]

Thanks!