What are the rules for drawing electric field patterns?
Answers
There are a variety of conventions and rules to drawing such patterns of electric field lines. The conventions are simply established in order that electric field line patterns communicate the greatest amount of information about the nature of the electric field surrounding a charged object. One common convention is to surround more charged objects by more lines. Objects with greater charge create stronger electric fields. By surrounding a highly charged object with more lines, one can communicate the strength of an electric field in the space surrounding a charged object by the line density. This convention is depicted in the diagram below.
Not only does the density of lines surrounding any given object reveal information about the quantity of charge on the source charge, the density of lines at a specific location in space reveals information about the strength of the field at that location. Consider the object shown at the right. Two different circular cross-sections are drawn at different distances from the source charge. These cross-sections represent regions of space closer to and further from the source charge. The field lines are closer together in the regions of space closest to the charge; and they are spread further apart in the regions of space furthest from the charge. Based on the convention concerning line density, one would reason that the electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge. Line density in an electric field line pattern reveals information about the strength or magnitude of an electric field.
A second rule for drawing electric field lines involves drawing the lines of force perpendicular to the surfaces of objects at the locations where the lines connect to object's surfaces. At the surface of both symmetrically shaped and irregularly shaped objects, there is never a component of electric force that is directed parallel to the surface. The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. If there were ever any component of force parallel to the surface, then any excess charge residing upon the surface of a source charge would begin to accelerate. This would lead to the occurrence of an electric current within the object; this is never observed in static electricity. Once a line of force leaves the surface of an object, it will often alter its direction. This occurs when drawing electric field lines for configurations of two or more charges as discussed in the section below.
A final rule for drawing electric field lines involves the intersection of lines. Electric field lines should never cross. This is particularly important (and tempting to break) when drawing electric field lines for situations involving a configuration of charges (as in the section below). If electric field lines were ever allowed to cross each other at a given location, then you might be able to imagine the results. Electric field lines reveal information about the direction (and the strength) of an electric field within a region of space. If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location. This could never be the case. Every single location in space has its own electric field strength and direction associated with it. Consequently, the lines representing the field cannot cross each other at any given location in space.