deletions | additions       diff --git a/Physical_model.tex b/Physical_model.tex  index 5e0385e..6554621 100644  --- a/Physical_model.tex  +++ b/Physical_model.tex 
...
We set up an experiment illustrated in Figure \ref{Figure1}-(A). The key components are as follows: a coil induces an electrical current $\mathbf{j}$ in the sample; a magnet creates a magnetic field $\mathbf{B}$; an ultrasound probe tracks displacements $\mathbf{u}$ propagating as shear waves in the sample. X is defined as the main magnetic field axis, Z as the main ultrasound propagation axis, and Y an axis orthogonal to X and Z following the right-hand rule. The origin of coordinates (0,0,0) is located in the middle of the butterfly coil (i.e., between the two loops).  For a circular coil centered in (0,0,0) of linear element $\mathbf{dl}$ $d\mathbf{l}$  crossed by an electrical current $I(t)$, using Coulomb gauge (i.e., $\nabla . \mathbf{A} = 0$ where $\mathbf{A}$ is the magnetic potential vector), and negligible propagation time of electromagnetic waves, the electrical field $\mathbf{E}(\mathbf{r},t)$ along space $\mathbf{r}$ and time $t$ is equal to \cite{jackson1998classical}: \begin{equation}  \mathbf{\mathbf{E(\mathbf{r},t)}} = - \nabla \Phi - \frac{d I}{d t} \frac{N \mu_0}{4\pi}\int{\frac{\mathbf{dl}}{r}}  \label{Equation1}