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I'm trying to understand the concept of electric potential and the significance of an electric field being related to the gradient/derivative of an electric potential.

I found this question that explains how potential energy relates to force in the $-z$ direction - Is force the derivative of energy?

What would an analogous answer be for electric potential and force in one dimension?

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  • $\begingroup$ Potential energy by defintion is $F=- \dfrac{dU}{dr}$. Where $F$ is the force, $U$ is potential energy and $r$ is position. $\endgroup$
    – Omar Nagib
    Commented Apr 28, 2016 at 16:20

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The analogy would be voltage as the potential, so this would be analogous to height (as in the height of a rock of mass m in gravity field g).

Since power (which is also energy) is Voltage x Amps, then Amperes is analogous to mg. If you want to break it down further, I guess mg = Q/sec.

I'm not sure if this answers your question, but it at least gets things started.

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