# Electrostatic Potential Definition

In the book, Introduction to electrodynamics by David J. Griffiths, he introduces potential separately as a function and potential energy through that function.

How can potential be defined before defining potential energy? Isn't the potential just potential energy per unit charge? How can potential mean something on its own?

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– Qmechanic Apr 25 '13 at 21:45

The electric field is a conservative vector field which implies that there exists a function $V$ for which $$\mathbf E = -\nabla V$$ We call this function $V$ the electric potential. There is no mathematical need to first define potential energy. One can then physically interpret $V$ in terms of a "potential landscape" to get intuition for what it means. In particular, positive charges "roll down" potential hills while negative charges "roll up potential hills." But from a mathematical point of view, there is no need for the intermediate definition of potential energy.