Changes between Version 11 and Version 12 of u/erica/d


Ignore:
Timestamp:
12/14/15 14:01:34 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/d

    v11 v12  
    5252
    5353[[latex($0 = -\bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{B^2}{\mu} \frac{\hat{\bold{n}}}{r}$)]]
     54
     55Now, projecting this equation onto the r-axis gives n-hat = -r-hat, and thus we have:
     56
     57[[latex($-\frac{d}{dr}(\frac{B^2}{2 \mu}) \hat{\bold{r}} = \frac{B^2}{\mu r} \hat{\bold{r}}$)]]
     58
     59The solution to this differential equation is:
     60
     61[[latex($B^2 = B_0^2(\frac{r_0}{r})^2$)]]
     62
     63where the field is the initial value in the un-perturbed medium beyond the ring's outer radius !r0.