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 # Electromagnetic FEA Simulations
 
+<script type="math/tex; mode=display">\sum_{n=1}^\infty \frac{(ik)^n}{n!} C_n = \log \langle e^{ikx} \rangle</script>
+
 We can create rudimentary 2D and 3D FEA simulations of current carrying wires and permanent magnets in free space using only two equations: 
 
 For current carrying wires we use [Biot-Savart](https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law):
@@ -18,7 +20,7 @@ The rest is surprisingly simple and can be implemented in about 100 lines of cod
 
 ![alt_text](images/diySim1.png "diySim1")
 
-Examining the results above, there are some innacuracies and limitations worth noting for improvement:
+Examining the results above, there are some inaccuracies and limitations worth noting for improvement:
 
 1) First let's note that there appears to be divergence on the left and right bounds of the permanent magnet where the field changes direction. I initially assumed that this was incorrect, but it turns out [H fields are indeed divergent](https://en.wikipedia.org/wiki/Magnetic_field#H-field_and_magnetic_materials) at the boundary of a magnet, and [Gauss's law for magnetism](https://en.wikipedia.org/wiki/Gauss%27s_law_for_magnetism) applies to magnetic flux density B, but not field strength H. This should really be apparent from the fact that H = B/u_0 - M, where the magnetization vector M is just a uniform vector field that sources from one side of the magnet and sinks into the other, as shown in the image linked to above.
 
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