An open regular surface is characterised by a surface vector. Its orientation is defined by orientation rules: The right hand rule and the corkscrew rule are two of them.

One uses the right-hand rule to determine the orientation of a vector surface. Some people speak also of the "corkscrew rule"

2D illustration of the link between electric field and electric potential. The grad(V) vector is computed at every point of a geometric matrix the interval values of which you can modify.

Gauss's theorem applied to an infinite and uniformly charged cylinder or line. The choice of a cylinder that is closed at both ends as the closed surface enables one to act judiciously where the lines of electrical force are concerned.

Gauss's theorem applied to a uniformly charged sphere, illustrating the calculation of Qint. Using a closed Gauss surface allows a simple calculation if it relies judiciously on the symmetries of the field. In our case, the closed surface is a sphere with no material reality.

Gauss's theorem is always valid. We can apply it to any closed surface and the calculated flux will depend exclusively on the charge within the closed surface.

The electric force vector points in the direction in which V decreases and remains perpendicular  to the equipotentials. The common trajectory of a particle experiencing such a field is an ellipse similar to gravitational orbits. This is a conservative force.

You can catch and “throw” the moving particle to change the initial conditions.

The flux through a surface is derived from integral calculus. This animation shows the surface vectors of three small pieces of surface, "dS", randomly chosen on a closed surface. This is an algebraic value: the first is negative, the second is positive and the last one is equal to zero.

This animation illustrates the connection between electric lines of force and Voltage Equipotentials. The spherical symmetry of this charge distribution is revealed by its spherical equipotentials. The field is orthogonal to these equipotentials at any point and always points in the direction of decreasing potential.

This animation illustrates the connection between electric lines of force and Voltage Equipotentials. The spherical symmetry of this charge distribution is revealed by its spherical equipotentials. The field is orthogonal to these equipotentials at any point and always points in the direction of decreasing potential.