deletions | additions       diff --git a/magnetoresistance.tex b/magnetoresistance.tex  index 45063ef..6781e9b 100644  --- a/magnetoresistance.tex  +++ b/magnetoresistance.tex 
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\begin{equation}  \mathbf{B} = \left(0, 0, B\right)  \end{equation}  Since any current parallel to the magnetic field will not be affected, let's take both the electric field $\mathbf{E}$  and current $\mathbf{j}$  to lie in the $x$--$y$ plane.\footnote{We can simply do so by setting $E_z$ to zero. In the absence of a $z$ component of the electric field, no current will flow in the $z$ direction. The same is not true with the $x$ and $y$ direction, since the magnetic field will result in a nonzero component of the current in a direction perpendicular to the electric field.} Therefore, \begin{equation}  \begin{split}  \mathbf{j} &= \left(j_x, j_y, 0\right) \\  \mathbf{E} &= \left(E_x, E_y, 0\right)  \end{split}  \end{equation}   Substituting the components of $\mathbf{B}$, $\mathbf{E}$ and $\mathbf{j} = n q \mathbf{p} / m^*$ into the equation of motion for the charge carrier in the presence of a magnetic field \eqref{eq:eom-B} gives:   \begin{equation}   \begin{split}   j_x = \frac{\sigma_0}{1 + (\omega_C \tau)^2} \, E_x + \frac{\sigma_0 \omega_C \tau}{1 + (\omega_C \tau)^2} \quad \textrm{, where}   \end{split}   \end{equation}   \begin{equation}  \end{equation}