Four equal point charges at tetrahedron vertices. Figure 1.3(a) shows four point charges...

Four equal point charges at tetrahedron vertices. Figure 1.3(a) shows four point charges Q = 1 nC positioned in free space at four vertices of a regular (equilateral) tetrahedron with the side length a = 1 cm. Using MATLAB, find the resultant electric

Force on one of the charges – for example, on the charge at the top of the tetrahedron. (ME1 5.m on IR) H⁵

HINT: Apply the program written in the previous MATLAB exercise, with N = 3, charges 1, 2, and 3 in Fig.1.3 (a) as the “source” charges, and charge 4 as the “target” charge. In particular, place the origin of the Cartesian coordinate system at the center of the base of the tetrahedron [point O in Fig.1.3 (a)]. To determine the coordinates of the charges, note that the distance b between charge 1 and point O and, from it, the height H of the tetrahedron are [the orthocenter of an equilateral triangle partitions its heights (h) into segments 2h/3 and h/3 long, where h = √ 3a/2]

As a result of computation, the plot of individual forces on the top charge due to the three charges at the tetrahedron base and the total force should look like the one in Fig.1.3 (b). By means of the rotation button in the MATLAB figure, rotate the 3-D visualization of the solution to better see the forces and the geometrical representation of the problem. Finally, invoking Eq.(1.1) and the superposition principle, obtain the analytical expression for Fe4 and validate the MATLAB result against that expression.