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Benedict Irwin edited 4-Dimensions.tex
over 9 years ago
Commit id: dcd885912fcd7c60a1dc7cd824948997b88740e0
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\end{equation}
That is the electric field corresponds to the cross product of the spatial comonents of the four vectors, and that the magnetic field is the determinants of spatial components with time.
The elements of $B$ are signed areas of the parallellograms made in each basis direction $x,y,z$.
\begin{equation}
\nabla\cdot\textbf{B}=
\frac{\partial}{\partial x}\begin{vmatrix} t_1 & x_1 \\ t_2 & x_2 \end{vmatrix}+
\frac{\partial}{\partial y}\begin{vmatrix} t_1 & y_1 \\ t_2 & y_2 \end{vmatrix}+
\frac{\partial}{\partial z}\begin{vmatrix} t_1 & z_1 \\ t_2 & z_2 \end{vmatrix}
\end{equation}