Question 4.12: Using MATLAB, plot the voltage V(x) = e^-x² and the electric...

Fundamentals of Electromagnetics with MATLAB

Using MATLAB, plot the voltage $V(x) = e^{ -x^{2}}$ and the electric field $E_{x}(x) = -dV / dx$ as a function of x in the range – 3 ≤ x ≤ 3.

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The difference operation diff(V)./diff(x) sequentially performs and stores the values

\left\{\frac{V(2) – V(1)}{h} , \frac{V(3) – V(2)}{h},…,\frac{V(n) – V(n-1)}{h}\right\}

There are only (n – 1) values of the derivatives. Therefore, if we wish to plot the results, we plot V in the range $x_{0}$ to $x_{b}$ at increments of h and dV / dx in the range $x_{a} + h / 2$ to $x_{b} – h / 2$ with the same increment h. The plots of the potential and the electric fields are shown in the figure below.

4.12

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