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This app visualises vector fields in 2D and 3D.

Select a preset field from the dropdown, or enter custom component expressions in the text boxes.

Selecting Point gives the vector field at a particular point.

In 2D mode, toggle ∇·F (divergence) or ∇×F (curl) to overlay a heat map or contour plot of the corresponding scalar field.

Overview

A vector field F assigns a vector to each point in space.

The divergence ∇·F measures how much the field spreads out or converges at a point. In 2D:

∇·F = ∂F_x/∂x + ∂F_y/∂y

The curl ∇×F tells us how the vector field swirls/rotates. In 2D only the z-component is non-zero:

(∇×F)_z = ∂F_y/∂x − ∂F_x/∂y