Electric Field Flux and Lines of Force Principles

Electric Field Flux and Gaussian Surfaces

The flow of an electric field through a Gaussian surface, also known as electric flux (symbol Φ), is a property of any vector field referring to a hypothetical surface that can be closed or open. For an electric field, the flow (Φe) is measured by the number of lines of force crossing the surface.

To define Φe precisely, consider an arbitrary closed surface within an electric field. The surface is divided into elementary squares (ΔS), each of which is small enough so it can be considered flat. These area elements can be represented as vectors ΔS, whose magnitude is the area itself, the direction is normal to the surface, and the orientation is towards the outside. For each elementary square, it is also possible to draw an electric field vector (E). Since the squares are as small as desired, E can be considered constant at all points of a given square. E and ΔS characterize each square and form an angle between each other; the figure shows a magnified view of two squares.

Understanding Lines of Force in Electric Fields

It is possible to obtain a graphical representation of a force field using the so-called lines of force. They are imaginary lines that describe changes in the direction of forces when moving from one point to another. In the case of the electric field, since it has both magnitude and direction, it is a vector quantity. The lines of force, or electric field lines, indicate the paths that positive particles would follow if they were left free under the influence of the field's forces. The electric field is a vector tangent to the line of force at any point considered.

Field Maps and Charge Interactions

• Positive Point Charges: These result in a map of radial lines of force because electric forces always act in the direction of the line joining the interacting charges. They are directed outward because mobile positive charges would move in that direction due to repulsive forces.
• Negative Point Charges: In the case of a field due to a negative point charge, the map of lines of force is similar but directed toward the central charge.
• Multi-Charge Fields: In fields involving multiple charges, the force lines always originate from positive charges and terminate at negative charges. In physics terminology, positive charges are considered "sources" and negative charges are "sinks" of lines of force.