#area element

Unpacking the fundamental theorem of multivector calculus in two dimensions

Notes. Due to limitations in the MathJax-Latex package, all the oriented integrals in this blog post should be interpreted as having a clockwise orientation. [See the PDF version of this post for more sophisticated formatting.] Guts. Given a two dimensional generating vector space, there are two instances of the fundamental theorem for multivector…

Generalizing Ampere’s law using geometric algebra.

[Click here for a PDF of this post with nicer formatting, and oriented integrals. All oriented integrals in this post have a clockwise direction.].

The question I’d like to explore in this post is how Ampere’s law, the relationship between the line integral of the magnetic field to current (i.e. the enclosed current) \begin{equation}\label{eqn:flux:20} \oint_{\partial A} d\Bx \cdot \BH =…

Stokes integrals for Maxwell’s equations in Geometric Algebra

[Click here for a PDF of this post with nicer formatting]

Recall that the relativistic form of Maxwell’s equation in Geometric Algebra is

\begin{equation}\label{eqn:maxwellStokes:20} \grad F = \inv{c \epsilon_0} J. \end{equation}

where \( \grad = \gamma^\mu \partial_\mu \) is the spacetime gradient, and \( J = (c\rho, \BJ) = J^\mu \gamma_\mu \) is the four (vector) current density. The…