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I’m looking for a qualitative explanation for why electric field strength is the negative of potential gradient.

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  • $\begingroup$ How can I improve this question? $\endgroup$ Commented Jun 28, 2020 at 14:53

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In fact, it is not. However, $\vec{E}=-\nabla V$ is correct. It is because of the definition of the potential: $V(\vec{r})=-\int_P^\vec{r} \vec{E}\cdot d\vec{l}$, i.e. the line integral of the electric field with $P$ some reference point.

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  • $\begingroup$ Why do you say “it is not”? Are you interpreting “electric field strength” to mean $|\vec E|$? I doubt that this is what the OP meant by that phrase. $\endgroup$
    – G. Smith
    Commented Jun 28, 2020 at 17:04

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