From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 source/know/concept/magnetic-field/index.md | 68 ++++++++++++++---------------
 1 file changed, 34 insertions(+), 34 deletions(-)

(limited to 'source/know/concept/magnetic-field')

diff --git a/source/know/concept/magnetic-field/index.md b/source/know/concept/magnetic-field/index.md
index 369c8a6..8d215fb 100644
--- a/source/know/concept/magnetic-field/index.md
+++ b/source/know/concept/magnetic-field/index.md
@@ -8,28 +8,28 @@ categories:
 layout: "concept"
 ---
 
-The **magnetic field** $\vb{B}$ is a vector field
+The **magnetic field** $$\vb{B}$$ is a vector field
 that describes magnetic effects,
 and is defined as the field that correctly predicts
 the [Lorentz force](/know/concept/lorentz-force/)
-on a particle with electric charge $q$:
+on a particle with electric charge $$q$$:
 
 $$\begin{aligned}
     \vb{F}
     = q \vb{v} \cross \vb{B}
 \end{aligned}$$
 
-If an object is placed in a magnetic field $\vb{B}$,
+If an object is placed in a magnetic field $$\vb{B}$$,
 and wants to rotate to align itself with the field,
-then its **magnetic dipole moment** $\vb{m}$
-is defined from the aligning torque $\vb{\tau}$:
+then its **magnetic dipole moment** $$\vb{m}$$
+is defined from the aligning torque $$\vb{\tau}$$:
 
 $$\begin{aligned}
     \vb{\tau} = \vb{m} \times \vb{B}
 \end{aligned}$$
 
-Where $\vb{m}$ has units of $\mathrm{J / T}$.
-From this, the **magnetization** $\vb{M}$ is defined as follows,
+Where $$\vb{m}$$ has units of $$\mathrm{J / T}$$.
+From this, the **magnetization** $$\vb{M}$$ is defined as follows,
 and roughly represents the moments per unit volume:
 
 $$\begin{aligned}
@@ -38,17 +38,17 @@ $$\begin{aligned}
     \vb{m} = \int_V \vb{M} \dd{V}
 \end{aligned}$$
 
-If $\vb{M}$ has the same magnitude and orientation throughout the body,
-then $\vb{m} = \vb{M} V$, where $V$ is the volume.
-Therefore, $\vb{M}$ has units of $\mathrm{A / m}$.
+If $$\vb{M}$$ has the same magnitude and orientation throughout the body,
+then $$\vb{m} = \vb{M} V$$, where $$V$$ is the volume.
+Therefore, $$\vb{M}$$ has units of $$\mathrm{A / m}$$.
 
-A nonzero $\vb{M}$ complicates things,
+A nonzero $$\vb{M}$$ complicates things,
 since it contributes to the field
-and hence modifies $\vb{B}$.
+and hence modifies $$\vb{B}$$.
 We thus define
-the "free" **auxiliary field** $\vb{H}$
-from the "bound" field $\vb{M}$
-and the "net" field $\vb{B}$:
+the "free" **auxiliary field** $$\vb{H}$$
+from the "bound" field $$\vb{M}$$
+and the "net" field $$\vb{B}$$:
 
 $$\begin{aligned}
     \vb{H} \equiv \frac{1}{\mu_0} \vb{B} - \vb{M}
@@ -56,24 +56,24 @@ $$\begin{aligned}
     \vb{B} = \mu_0 (\vb{H} + \vb{M})
 \end{aligned}$$
 
-Where the **magnetic permeability of free space** $\mu_0$ is a known constant.
+Where the **magnetic permeability of free space** $$\mu_0$$ is a known constant.
 It is important to point out some inconsistencies here:
-$\vb{B}$ contains a factor of $\mu_0$, and thus measures **flux density**,
-while $\vb{H}$ and $\vb{M}$ do not contain $\mu_0$,
+$$\vb{B}$$ contains a factor of $$\mu_0$$, and thus measures **flux density**,
+while $$\vb{H}$$ and $$\vb{M}$$ do not contain $$\mu_0$$,
 and therefore measure **field intensity**.
 Note that this convention is the opposite of the analogous
 [electric fields](/know/concept/electric-field/)
-$\vb{E}$, $\vb{D}$ and $\vb{P}$.
-Also note that $\vb{P}$ has the opposite sign convention of $\vb{M}$.
+$$\vb{E}$$, $$\vb{D}$$ and $$\vb{P}$$.
+Also note that $$\vb{P}$$ has the opposite sign convention of $$\vb{M}$$.
 
 Some objects, called **ferromagnets** or **permanent magnets**,
-have an inherently nonzero $\vb{M}$.
-Others objects, when placed in a $\vb{B}$-field,
-may instead gain an induced $\vb{M}$.
+have an inherently nonzero $$\vb{M}$$.
+Others objects, when placed in a $$\vb{B}$$-field,
+may instead gain an induced $$\vb{M}$$.
 
-When $\vb{M}$ is induced,
+When $$\vb{M}$$ is induced,
 its magnitude is usually proportional
-to the applied field strength $\vb{H}$:
+to the applied field strength $$\vb{H}$$:
 
 $$\begin{aligned}
     \vb{B}
@@ -83,20 +83,20 @@ $$\begin{aligned}
     = \mu \vb{H}
 \end{aligned}$$
 
-Where $\chi_m$ is the **volume magnetic susceptibility**,
-and $\mu_r \equiv 1 + \chi_m$ and $\mu \equiv \mu_r \mu_0$ are
+Where $$\chi_m$$ is the **volume magnetic susceptibility**,
+and $$\mu_r \equiv 1 + \chi_m$$ and $$\mu \equiv \mu_r \mu_0$$ are
 the **relative permeability** and **absolute permeability**
 of the medium, respectively.
 Materials with intrinsic magnetization, i.e. ferromagnets,
-do not have a well-defined $\chi_m$.
+do not have a well-defined $$\chi_m$$.
 
-If $\chi_m > 0$, the medium is **paramagnetic**,
-meaning it strengthens the net field $\vb{B}$.
-Otherwise, if $\chi_m < 0$, the medium is **diamagnetic**,
-meaning it counteracts the applied field $\vb{H}$.
+If $$\chi_m > 0$$, the medium is **paramagnetic**,
+meaning it strengthens the net field $$\vb{B}$$.
+Otherwise, if $$\chi_m < 0$$, the medium is **diamagnetic**,
+meaning it counteracts the applied field $$\vb{H}$$.
 
-For $|\chi_m| \ll 1$, as is often the case,
-the magnetization $\vb{M}$ can be approximated by:
+For $$|\chi_m| \ll 1$$, as is often the case,
+the magnetization $$\vb{M}$$ can be approximated by:
 
 $$\begin{aligned}
     \vb{M}
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