1. Introduction
This project has the goal of simulating an experiment involving electric current. A Visual Basic program will be created to display the propagation of electrons.
2. Discrete Space and Time
The magnitude of the electric and magnetic fields can be assigned to many small portions of space arranged in a 3-dimensional matrix. The computer can then store a floating-point value corresponding to electric and magnetic components of the vector field. This simulation will store charge and current densities for each "cell" of space in which the simulation will carry out its transition from one moment in time to the next. All behavior will be "local", so that a transition to a new state can be calculated deterministically from the current state of the cell, along with the states of its immediate neighbors.
3. Approximating Electic Current and a Magnetic Field
To simulate electric current, the charge densities of each neighboring cell will be included in a linear combination, so that charge carriers can flow through the material.
The current in the X and Y directions can be computed by comparing charge
density differences. By using the cross-product, the force on the charges
due to the Hall effect will be added into the array.
4. Results
As voltage is applied, the electrical charges propagate through the material, with a density that varies with distance from one side to the other. Additionally, applying a magnetic field illustrates an accumulation of charges along the Y-axis.
Screen Shot:
The following is the Visual Basic project:
hall.frm - Visual Basic Form declaration and source code