Charge

Electrostatic Calculation and Visualization

In physics, the space surrounding an electric charge has a property called an electric field. This electric field exerts a force on other charged objects. The concept of electric field was introduced by Michael Faraday.

This tutorial shows the GSSE and the graphical preparation of the electrical field of a point charge. First the field is calculated using GSSE methods, then you have to use a visualization mechanism to create a picture of the field.

Tasks

L1: Assign vertex values for the electric field as well as the electrostatic potential:

$\varphi(\mathcal{P}) = \frac{1}{4 \pi \varepsilon} \frac{q}{r_{\mathcal{P}\mathcal{Q}}}, \vec{E}(\mathcal{P}) = \frac{1}{4 \pi \varepsilon} \frac{q \vec{e_{\mathcal{P}\mathcal{Q}}}} {r_{\mathcal{P}\mathcal{Q}}^2}$

Use the mapped_type in order to store the values. In these formulae $r_{\mathcal{P}\mathcal{Q}}$ denotes the distance between the location of the point charge $\mathcal{Q}$ and the point of the field $\mathcal{P}$ . The unit vector $\vec{e_{\mathcal{P}\mathcal{Q}}}$ stands for the vector which points from $\mathcal{P}$ to $\mathcal{Q}$ .

L1: Implement a function which determines the euclidian norm of an arbitrary vector. Use this formula in order to determine the distance $r_{\mathcal{P}\mathcal{Q}}$ . The euclidian norm of a n-dimensional vector can be derived as

$\Vert\vec{r}\Vert = \sqrt{\sum_{i=1} ^{\mathrm{dim}(\vec{r})} r_i^2}$ .

For two dimensions the distance can be implemented as follows:

return std::sqrt(pnt[0]*pnt[0] + pnt[1]*pnt[1])

L2: Implement such a formula for the GSSE point type independently of its dimension.

L2: Implement a direction function. The unit vector of the direction can be implemented using the following formula: $\vec{e_{\mathcal{P}\mathcal{Q}}} = \frac{r_{\mathcal{P}\mathcal{Q}}} {\Vert r_{\mathcal{P}\mathcal{Q}} \Vert}$

L2: Next, implement the formulae for the potential as well as the electrical field. For this reason place the point charge

$\mathcal{Q}$ and insert values for q and $\varepsilon_0 = 8.854 \cdot 10^{-12}$ . Evaluate the formulae on all vertices.

L1: For the storage of the components of the electric field use two separate quantities.