Vector Field - Examples

Examples

• A vector field for the movement of air on Earth will associate for every point on the surface of the Earth a vector with the wind speed and direction for that point. This can be drawn using arrows to represent the wind; the length (magnitude) of the arrow will be an indication of the wind speed. A "high" on the usual barometric pressure map would then act as a source (arrows pointing away), and a "low" would be a sink (arrows pointing towards), since air tends to move from high pressure areas to low pressure areas.
• Velocity field of a moving fluid. In this case, a velocity vector is associated to each point in the fluid.
• Streamlines, Streaklines and Pathlines are 3 types of lines that can be made from vector fields. They are :

streaklines — as revealed in wind tunnels using smoke.

streamlines (or fieldlines)— as a line depicting the instantaneous field at a given time.

pathlines — showing the path that a given particle (of zero mass) would follow.

• Magnetic fields. The fieldlines can be revealed using small iron filings.
• Maxwell's equations allow us to use a given set of initial conditions to deduce, for every point in Euclidean space, a magnitude and direction for the force experienced by a charged test particle at that point; the resulting vector field is the electromagnetic field.
• A gravitational field generated by any massive object is also a vector field. For example, the gravitational field vectors for a spherically symmetric body would all point towards the sphere's center with the magnitude of the vectors reducing as radial distance from the body increases.