Skip to main content \(\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Section 28.3 Magnetic Flux
The definition you saw for
Electric Flux can be extended to define a new quantity called
magnetic flux .
Definition 28.3.1 . Magnetic flux.
Magnetic flux is a measure of how much magnetic field is passing perpendicularly through a surface:
\begin{equation*}
\mathit{\Phi}_{B} = \iint \vec{B}\cdot d\vec{A}
\end{equation*}
The double-integral sign indicates that the integral is over a two-dimensional surface, and the limits of integration must be chosen so that they cover the entirety of the desired surface. The differential area vector
\(d\vec{A}\) represents an infinitesimal piece of the total surface.
Subsubsection Activities
Activity 28.3.1 . Flux through a Book.
Suppose you have a region of space where the magnetic field is uniform and points entirely in the
\(y\) -direction with magnitude
\(B_1\text{.}\)
(a) Make a quick sketch of the magnetic field, including
\(x\) -,
\(y\) -, and
\(z\) -axes.
(b) Add the following two surfaces to your sketch:
Surface 1: A circle with radius
\(R\) in the
\(xy\) -plane.
Surface 2: A circle with radius
\(R\) in the
\(xz\) -plane.
(c) Sketch an area vector for each surface.
(d) Use your chosen area vectors and the given magnetic field to calculate the magnetic flux through each surface.
