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It's an image from my textbook where it's written that EPG is scalar but at some sites I read that it is vector.

enter image description here

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  • $\begingroup$ $dV/dr$ isn't a vector, but $\nabla V$ is. $\endgroup$
    – J.G.
    Oct 16, 2021 at 17:33

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The key here is that the text states "along a particular direction". The electric potential gradient, is in general, a vector quantity, but when on the component is a specific direction is considered it is a scalar. More mathematically what is being suggested here is that the quantity of interest is the projection of the potential gradient in specific direction and that is indeed a scalar.

Let $V$ be the electric potential, then the gradient, a vector, is the negative of the electric field: $-\vec{E} = \nabla V$.

The text's example is equivalent to $\hat{r}\cdot\nabla V$, where $\hat{r}$ is a unit vector in the specific direction and the result of the dot product of two vectors is a scalar.

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