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Hey,

I have a question about Electric Field/Electric Potential gradient notation.

Since,

[tex]

{\vec{E}} = {-}{\nabla}{V(r)}

[/tex]

Which reduces to,

[tex]

\vec{E} = {-}{\nabla}{V(x, y, z)}

[/tex]

When expanded is,

[tex]

\vec{E} = {-}{\left[{\frac{\partial[V]}{\partial{x}}}{\hat{i}} + {\frac{\partial[V]}{\partial{y}}}{\hat{j}} + {\frac{\partial[V]}{\partial{z}}}{\hat{k}}\right]}

[/tex]

So using partial derivative notation can I write,

[tex]

{\vec{E}} = {-}{\vec{V}'_{xyz}}

[/tex]

So, is the above correct notation?

The reason I am hesitant is, because formally the gradient is defined as a vector operator that takes a scalar field (such as the electric potential) and changes it to a vector field (such as the electric field) through: partial differentiation with the addition of unit vectors ([tex]\hat{i}, \hat{j}, \hat{k}[/tex]).

However, writing it as below sort of implies the potential is a vector (which it isn't), but gives the impression that it is because of how the gradient is defined.

[tex]

{\vec{E}} = {-}{\vec{V}'_{xyz}}

[/tex]

So, is the above notation correct?

-PFStudent

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# Electric Field/Electric Potential (Gradient Notation)

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