- #1
PFStudent
- 170
- 0
Homework Statement
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
Last edited: