Fields

Notes are here

Keyboard - a/s left right q/w in out e/d up down r reset

Scalar field





Vector field F








Fields

This is about scalar and vector fields in 2D.

A scalar field f can be defined and displayed, in red, in the left window. The field can be defined in terms of Cartesian co-ordinates f(x,y), or using polar co-ordinates f(r,θ). The x axis is red and y is yellow, and ranges + and - 10. The size of the scalar at any point is shown by the height above that point, on the red surface on the left.

The θ button can be used to enter theta into a polar definition.

With a scalar field f, we can show grad f, as a vector field with components δf/δx and δf/δy. This is shown as a set of arrow lines, black to orange, with direction grad f and length the magnitude of grad f at that (x,y) point. This is shown on the right over the x y plane, and on the left, attached to the f surface ( grad f is in fact all on the x y plane, since this is a 2D field).

We can also define and display a vector field F, with Cartesian components Fx and Fy, or in terms of polar co-ordinates, in green.

From a vector field F, we can display div F, as partial ∂Fx/∂x + ∂Fy/∂y. This is a scalar, displayed as a yellow surface on the left.

We can also display curl F, defined as partial ∂Fy/∂x - ∂Fx/∂y, as a blue surface. This is a scalar, while in 3D curl is a vector.

Some keys alter the 'camera' position. q and w move forward and backward along the x axis (as it rotates).
a and s move along y, z and x move on 'z' = above and below xy plane.
The camera remains pointing at (0,0)