Martin Luther King's iconic I Have a Dream speech is full of allusions. Let's look at a few: Dr. King's speech (1963) was made 100 years after Lincoln's Emancipation Proclamation (1863) that freed all slaves in rebel territories.
There are a number of commercial packages you can use for such purposes. Comsol multiphysics simulation software is a general purpose physics modelling software package that I belive can deal with electromagnitism. The link to their website is http://www.uk.comsol.com. Ansys is another commercial vendor that provides a electromagnetic physics module. There website is http://www.ansys.com.
The magnetic force is, in effect, relaying the action from one circuit to another. The first circuit is called the control circuit; the second is called the load circuit. There are three basic functions of a relay: On/Off Control, Limit Control and Logic Operation. On/Off Control: Example: Air conditioning control, used to limit and control a high power.