Distances

The vectors are found as the following below:

$\vec v_{nm} = p_n - p_m$

$\vec v_{12} =$ {{outputs.v1_2 | katex}}

$\vec v_{13} =$ {{outputs.v1_3 | katex}}

$\vec v_{23} =$ {{outputs.v2_3 | katex}}

$\vec v_{21} = -v_{12} =$ {{outputs.v2_1 | katex}}

$\vec v_{31} = -v_{13} =$ {{outputs.v3_1 | katex}}

$\vec v_{32} = -v_{21} =$ {{outputs.v3_2 | katex}}

Forces finding distance and unit vector

$d_{nm} = \sqrt{v_{nm_x}^2 + v_{nm_y}^2}$

$\vec u_{nm} = \frac{\vec v_{nm}}{|\vec v_{nm}|} = \frac{\vec v_{nm}}{d_{nm}}$

The force between each pair of charges is then found through Coulomb's Law:

$\vec F_{nm} = k\frac{q_nq_m}{d^2} \vec{u}_{nm}$

$\vec F_{12} =$ {{outputs.F1_2 | katex}} $N$

$\vec F_{13} =$ {{outputs.F1_3 | katex}} $N$

$\vec F_{23} =$ {{outputs.F2_3 | katex}} $N$

$\vec F_{21} = -F_{12} =$ {{outputs.F2_1 | katex}} $N$

$\vec F_{31} = -F_{13} =$ {{outputs.F3_1 | katex}} $N$

$\vec F_{32} = -F_{21} =$ {{outputs.F3_2 | katex}} $N$

{% for i in range(outputs.Fvect | length) %}

{% set electrostatic_eq = "\\vec F_" + (i+1) + " = " + outputs.F[i] + "N \\angle" + outputs.Angle[i] + "^{\\circ} = " + outputs.Fvect[i] + "N" %}

The total force is simply the summation of the point Forces between pairs:

{{electrostatic_eq | katex}}

{%endfor%}