Magnetic-Field-Structure-Related Concepts

Abstract

A magnetic field line (or “line of force”) is by definition a curve whose tangent at any point is parallel to the magnetic field-vector B. This property can be translated into mathematical terms as follows:

$$ B\alpha dR\;or\;B = c\,dR $$

(4.1.1)

where c is a proportionality constant and dR is a differential vector tangent to the field line (R is the position vector from a chosen origin to the point in question on the curve). Equivalently

$$ B \times dR = 0 $$

(4.1.2)