Our present understanding of electrical properties relies on the notions of fields and waves. A field, loosely speaking, is a mathematical "map" of forces, specifying their directions and strengths. An equation, or several of them together, can be solved for the force values at any point or succession of points within the field.

The attraction of unlike charges, or the repulsion of like charges, has a simple field interpretation: you may imagine every charge as the center of its own field and interacting with other charges as if connected by invisible lines of force—in the case of attracting charges, as if they were attached to opposite ends of a stretched rubber band. The field math gives an answer, in volts, for how tight the rubber band is, how hard it is trying to pull the two charges together.

Charges carry their own magnetic force, too. These fields all have two ends, or poles, just like familiar representations of bar magnets. Every field line springs through space from one pole to another—in a smooth arc, if there are no other magnetic influences present to tug or distort the field. Whenever many fields are present, the overall picture may become a chaotic welter of contours and eddies.