Physics · Ch 10 — Electrostatics
Electric Lines of Force
Electric Lines of Force
Michael Faraday (1791-1867) introduced the concept of lines of force as a way to visualise both electric and magnetic fields. An ELECTRIC LINE OF FORCE is an imaginary curve drawn in a field such that the TANGENT to the curve, at any point along it, gives the DIRECTION of the electric field at that exact point (Fig. 10.11). Physically, if a small free positive test charge were released at rest somewhere in the field, the path it would trace out as it accelerates under the local Coulomb force at every instant is precisely a line of force.
The DENSITY of field lines -- how closely packed together they are drawn in a given region -- indicates the relative STRENGTH of the electric field there (Fig. 10.12): lines crowded closely together represent a strong field, while lines spread widely apart represent a weak one.
Electric lines of force obey a set of characteristic properties, all of which follow logically from the basic definition above: (1) lines of force ORIGINATE on a positively charged object and TERMINATE on a negatively charged object (Fig. 10.13 a,b,c); (2) lines of force never intersect or cross each other, since an intersection would mean the electric field has two different directions at the very same point, which is physically impossible for a well-defined field; (3) lines of force leave or terminate on a conductor's surface at right angles (NORMAL to the surface), never at a glancing angle; (4) lines of force never pass through the interior of a conductor at all, since the electric field inside a conductor in electrostatic equilibrium is always exactly zero -- though they DO pass freely through insulators; (5) the magnitude of the electric field at any point is proportional to the number of lines of force passing per unit area of a surface held perpendicular to the field there; (6) lines of force are drawn CROWDED together in any region where the field intensity is large; (7) lines of force are drawn WIDELY SEPARATED in any region where the field intensity is small (Fig. 10.13f compares two such regions directly); (8) for a UNIFORM electric field specifically, the li …
What this figure shows. A single curved line drawn through an electric field region, with a small arrow (tangent line) drawn touching the curve at one marked point along it, pointing in the direction of the local electric field at that point. The figure is the basic definition-diagram of a line of force: whatever the curve's overall shape, the direction of E at any point on it is always given by the TANGENT to the curve at that exact point, not by …
What this figure shows. Two regions are compared side by side (or two zones of one diagram): one region where field lines are drawn closely spaced/crowded together, labelled as the HIGH-field zone, and another where the same total number of lines are drawn more widely spread apart, labelled as the LOW-field zone. The figure establishes the rule that the NUMBER of field lines crossing a given unit area, held perpendicular to the field, is proportional to the field's magnitude there -- crowded lines mean strong field, sparse …
What this figure shows. A composite of six labelled panels showing standard field-line patterns: (a) lines radiating straight OUTWARD in all directions from an isolated POSITIVE point charge; (b) lines converging straight INWARD toward an isolated NEGATIVE point charge from all directions; (c) lines curving from a positive charge across to a nearby negative charge (an opposite-charge/dipole-like pair), each line leaving the positive charge and curving around to terminate on the negative charge; (d) lines for two charges of the SAME (similar) sign placed near each other, curving away from each other so that no line from one charge ever reaches the other, with a null point of zero field visible between them where lines from the two charges effectively cancel; (e) field lines shown terminating perpendicular (normal) to the surface of a nearby conductor, illustrating that lines always meet a conductor's surface at right angles and never run along it; (f) a comparison panel with two marked regions, A (where lines are drawn closely bunched, 'more lines cross the area at A') and B (where the same-sized area shows fewer, more widely spaced lines, 'l …