Field line

A field line is a curve tangent at every point to the direction of a vector field. Its pattern visualizes the field’s direction and, by line spacing, often its relative strength.

Connect

Vector field: A vector field assigns a vector to each point in a region of space. Field lines are curves defined by the directions of vectors at each point.
Electric field: An electric field is the force per unit positive charge at each point in space. Electric field lines show the direction a positive test charge would be pushed.
Equipotential surface: An equipotential surface is a surface on which a scalar potential has the same value everywhere. It represents a field through constant potential rather than curves following vector direction.
Tangent: A tangent is a line or vector giving the direction of a curve at a particular point. The tangent direction at each point is the defining condition for a field line.
Integral curve: An integral curve is a curve whose tangent vectors match a vector field along the curve. It is the mathematical object described by the field-line tangent rule.
Magnetic field: A magnetic field describes magnetic forces and effects at points in space. Magnetic field lines depict its local direction and the relative concentration of its strength.
Electric flux: Electric flux measures the electric field passing through a specified surface. Flux quantifies field passage mathematically, unlike a diagram’s chosen number of lines.
Scalar field: A scalar field assigns a numerical value to every point in a region. A scalar field can generate a vector field through its gradient, but is not itself traced by field lines.
Ordinary differential equation: An ordinary differential equation relates an unknown function to its derivatives. Tracing a field line amounts to solving an equation for a curve tangent to the field.
Magnetic field of Earth: Earth's magnetic field is the magnetic field generated mainly by motions in its liquid outer core. Its field-line pattern helps represent the planet's large-scale magnetic geometry.