Section 9.19 Determining E from V
Exercises Warm-Up Activity
1.
Given the equation you learned about in the previous section,
Principle 9.18.1, 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 9.19.1. 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*}
