Lines of Force

Faraday, Maxwell, Einstein

field, force, wave, particle

shape, pattern of force field

energy to matter, simple to complex

attraction, repulsion

Faraday coined the term lines of force.
Maxwell used the term tubes of force and compared electromagnetic force to fluid dynamics.

blender force fields: force, charge, magnetic, harmonic, collision, gravity

Particles, two types: hair and emission.

torus - a geometry surface generated by revolving a circle about an axis, creating a donut-shaped tube.

parts of a torus:

• tube
• central void
• axis of revolution
• circle, revolved around the axis, creating the tube

a torus is defined by two radii:

• $R =$ the major radius, from the axis to the center of the circle
• $r =$ the minor radius, the radius of the circle

types of torus, based on the aspect ratio between the two radii:

• $R > r =>$ torus of revolution - normal donut shape, axis does not touch the circle
• $R = r =>$ horn torus - axis is tangent to the circle
• $R < r =>$ spindle torus - self-intersecting, axis passes twice through the circle

• poloidal direction, red arrow, toward the poles, ring around the surface
• toroidal direction, blue arrow, parallel to lines of latitude

Note that:

• $R+r =$ radius of the outer rim of the tube
• $R-r =$ radius the inner rim of the tube

There are two ways to draw a spiral on the surface of a torus.

1. poloidal winding, a cylindrical helix drawn around the tube
2. toroidal winding, a closed helical trajectory drawn perpendicular to the axis

where $n = $ number of windings

StackExchange: Do these equations create a helix wrapped into a torus? (math for poloidal winding

“closed helical trajectory drawn along the surface of a torus”

Torus helix radius change equation (math for toroidal winding)
YouTube: toroidal winding built in Grasshopper

Steering Chiral Swimmers along Noisy Helical Paths

Transluminal Energy Quantum (TEQ) Model of the Electron