Changes between Version 11 and Version 12 of u/erica/d
- Timestamp:
- 12/14/15 14:01:34 (9 years ago)
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u/erica/d
v11 v12 52 52 53 53 [[latex($0 = -\bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{B^2}{\mu} \frac{\hat{\bold{n}}}{r}$)]] 54 55 Now, 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 59 The solution to this differential equation is: 60 61 [[latex($B^2 = B_0^2(\frac{r_0}{r})^2$)]] 62 63 where the field is the initial value in the un-perturbed medium beyond the ring's outer radius !r0.