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Section 24.3 Determining E from V
Exercises Warm-Up Activity
1. Given the equation you learned about in the previous section,
Determining Electric Potential Difference from Electric Field , suppose you instead knew the electric potential (
\(V\) ), and you wanted to figure out the electric field (
\(\vec{E}\) ). What mathematical operation could you perform on
\(V\) to get
\(\vec{E}\text{?}\)
Now you have seen how we can go back and forth between
\(V\) and
\(\vec{E}\text{.}\) To find
\(V\) from
\(\vec{E}\text{,}\) you can take a derivative!
Definition 24.3.1 . Electric Field: \(\vec{E}\) from V.
The electric field can be directly calculated given a known electric potential using the equation
\begin{equation*}
\vec{\mathit{E}} = -\vec{\nabla}\mathit{V}
\end{equation*}
