Physics · Ch 1 — Electrostatics
Electric field lines
Electric field lines
An electric field line is an imaginary curve, introduced by Faraday, drawn so that the tangent to the curve at any point gives the direction of the electric field at that point. Field lines are a pictorial (visualisation) tool, not physical entities; nonetheless they are extremely useful in electrostatics, because several important properties of the field can be read directly from a field-line diagram. Field lines begin on positive charges (or come in from infinity) and end on negative charges (or go out to infinity); for an isolated point charge, the lines are straight and radiate uniformly outward (positive charge) or inward (negative charge) in every direction. The number of field lines drawn per unit cross-sectional area (their density) is directly proportional to the field's magnitude at that location: field lines drawn close together indicate a strong field, and field lines drawn far apart indicate a weak field, which is why the lines of an isolated point charge, radiating outward and spreading over an ever larger sphere, thin out with distance in exactly the way the field magnitude itself falls off as 1/r^2. Two field lines can never cross one another, because the electric field has one and only one direction at any given point in space, and a crossing would require two different directions to exist there simultaneously. Field lines never form closed loo …
What this figure shows. For an isolated positive point charge, straight field lines are drawn radiating symmetrically outward in every direction like the spokes of a wheel, extending to infinity; for an isolated negative point charge, the field lines instead point radially inward, converging on the charge from every direction. Both patterns are perfectly symmetric about the charge, reflecting the fact that an isolated point charge's field has the same magnitude at every point on any sphere centred on it and always points directly along the radius, either outward (positiv …
What this figure shows. A single curved field line is drawn passing through a point P, together with a short straight arrow tangent to the curve exactly at P, representing the field vector E at that point. The figure establishes the defining geometric rule for reading any field-line diagram: the direction of the electric field at any point in space is given by the tangent drawn to the field line passing through that point, not by the …
What this figure shows. Two regions along a set of field lines are compared: one where several field lines pass close together through a small cross-sectional area, and another farther from the source where the same number of lines have spread apart to pass through a much larger area. The closely-packed region is where the field is strongest, and the widely-spaced region is where it is weakest, giving field-line density (the number of lines crossing a unit area perpendicular to them) a direct visual meaning as a stand-in for field …
What this figure shows. Two field lines are drawn as if they crossed at a single point, with a dashed circle highlighting that crossing point and two different tangent directions marked there to show the contradiction. If field lines truly crossed, the electric field at that shared point would simultaneously have two different directions, which is impossible for a single vector quantity at one location; hence real field lines can converge, diverge, or curve smoothly, but two distinct field lines can never actu …
What this figure shows. Field-line patterns are drawn for two side-by-side charge configurations: one showing two equal-and-opposite charges (a positive charge and a negative charge close together), whose lines emerge from the positive charge and curve around to terminate on the negative charge; the other showing two equal like charges (both positive, or both negative), whose lines emerge from each charge and bow apart from each other, refusing to link the two charges together, with a null point of zero field between them where the two contributions exactly cancel. The two contrasting patterns visually distinguish attraction (opposite charges, connected field li …