Definition 22.3.1. Electric Flux.
The electric flux, \(\mathit{\Phi}_E\text{,}\) through a surface defined by infinitesimal area vector \(d\vec{A}\) is given by 1
\begin{equation*}
\mathit{\Phi}_E = \iint\vec{E}\cdot d\vec{A}
\end{equation*}
Section 22.3 Electric Flux
Flux can be described as how much of something flows perpendicularly through an area. Common examples of flux might be how much water flows through the surface of your faucet, how many photons travel through the opening of a telescope, or how much wind flows through a window. We can also think about the electric flux:
The electric flux tells us about the total electric field passing perpendicularly through a surface. While the electric field isn’t actually "flowing" through a surface, it is still useful to discuss how much of the electric field is passing through a surface. The integral above is called a surface integral, and can be thought of as summing the electric flux passing through each infinitesimal \(d\vec{A}\text{.}\)
Exercises Activities
Recall Book Figure from Area Vectors for a Book.
1.
Suppose the book were placed in a region with a uniform electric field that points upward: \(\vec{E} = E_o\hat{y}\text{.}\) If the area of the front cover is \(A\text{,}\) determine the electric flux through the front cover. What happens to the integral in a case like this?
2.
Suppose you know the electric field everywhere in space and your surface of interest is the surface of a sphere centered on the origin. What is the area vector for this surface? Outline a general procedure for finding the electric flux through this surface. Can you think of any electric fields for which this procedure will be very challenging? Very easy?
After you have completed the activities above, watch the video below.
