Changes between Version 1 and Version 2 of u/erica/d


Ignore:
Timestamp:
12/05/15 13:55:17 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/d

    v1 v2  
    1111
    1212[[latex($(\bold{\nabla} \times \bold{B})\times \bold{B}=-\bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{1}{\mu}(\bold{B}\cdot \bold{\nabla}) \bold{B}$)]]
     13
     14the first term on the RHS is the same form as thermal pressure and so we call it the magnetic pressure. The second term is generally called the magnetic tension. To see why this is so, we rewrite it as:
     15
     16[[latex($\frac{1}{\mu}(\bold{B}\cdot \bold{\nabla}) \bold{B} = \hat{\bold{b}}\hat{\bold{b}} \cdot \bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{B^2}{\mu} \frac{\hat{\bold{n}}}{R_c}$)]]
     17
     18The first term on the RHS is a unit tensor dotted with the gradient of the magnetic pressure. The tensor is formed by the outer product of [[latex($\hat{\bold{b}}$)]] with itself. [[latex($\hat{\bold{b}}$)]] is the unit vector ''along'' the magnetic field line.