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Diffstat (limited to 'source/know/concept/alfven-waves')
| -rw-r--r-- | source/know/concept/alfven-waves/index.md | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/source/know/concept/alfven-waves/index.md b/source/know/concept/alfven-waves/index.md index 31576f3..0396c7a 100644 --- a/source/know/concept/alfven-waves/index.md +++ b/source/know/concept/alfven-waves/index.md @@ -61,12 +61,12 @@ $$\begin{aligned} = \frac{1}{\mu_0} \nabla \cross \vb{B}_1 \end{aligned}$$ -Substituting this into the momentum equation, +Substituting this into the above momentum equation, and differentiating with respect to $$t$$: $$\begin{aligned} \rho \pdvn{2}{\vb{u}_1}{t} - = \frac{1}{\mu_0} \bigg( \Big( \nabla \cross \pdv{}{\vb{B}1}{t} \Big) \cross \vb{B}_0 \bigg) + = \frac{1}{\mu_0} \bigg( \Big( \nabla \cross \pdv{\vb{B}_1}{t} \Big) \cross \vb{B}_0 \bigg) \end{aligned}$$ For which we can use Faraday's law to rewrite $$\ipdv{\vb{B}_1}{t}$$, @@ -78,7 +78,7 @@ $$\begin{aligned} = \nabla \cross (\vb{u}_1 \cross \vb{B}_0) \end{aligned}$$ -Inserting this into the momentum equation for $$\vb{u}_1$$ +Inserting this back into the momentum equation for $$\vb{u}_1$$ thus yields its final form: $$\begin{aligned} |