Editing Implicit surface (section)

=== Equipotential surface of point charges ===
{{Main article|Equipotential}}

The electrical potential of a point charge  <math>q_i</math> at point <math>\mathbf p_i=(x_i,y_i,z_i)</math> generates at point <math> \mathbf p=(x,y,z)</math> the potential (omitting physical constants)
: <math>F_i(x,y,z)=\frac{q_i}{\|\mathbf p -\mathbf p_i\|}.</math>
The equipotential surface for the potential value <math>c</math> is the implicit surface  <math> F_i(x,y,z)-c=0 </math> which is a sphere with center at point <math>\mathbf p_i</math>.

The potential of <math>4</math> point charges is represented by 
: <math>F(x,y,z)=\frac{q_1}{\|\mathbf p -\mathbf p_1\|}+ \frac{q_2}{\|\mathbf p -\mathbf p_2\|}+ \frac{q_3}{\|\mathbf p -\mathbf p_3\|}+\frac{q_4}{\|\mathbf p -\mathbf p_4\|}.</math>

For the picture the four charges equal 1 and are located at the points 
<math>(\pm 1,\pm 1,0)</math>. The displayed surface is the equipotential surface (implicit surface) <math>F(x,y,z)-2.8=0</math>.