Capacitor and Electrostatic Deflection Plate Model

Here the electric field of a square plate capacitor is calculated* on a set of cartesian grid points located at the base of each plotted arrow. As you can see, a cluster of near-parallel electric field field lines is created when the capacitor is charged. You can reorient the model by dragging the mouse over it for a clearer look at its three-dimensional structure. Puzzler #1: Which plate of this capacitor is positively charged, i.e. the one toward which or from which the larger electric field arrows point?

* (by integrating Coulomb's law dE=k_E dq r/r³ over the capacitor plate surfaces)

The capacitor design of course underlies the concept of capacitive circuit elements in electrical circuits. These play a key role in storing energy that will be needed in a hurry*, as well as in tuning electromagnetic broadcasts.

** (namely U = (1/2)C V², where capacitance C = Q/V ~ ε_o PlateArea/Spacing.)

The near constant field between such plates also makes them a natural component of electron beam devices which need to move electrons around at will (including the vacuum tube TV). The trajectory of such electrons may be calculated by integrating the force equation mx''=q E[x] over time from a given starting point and velocity. In regions where the electric field is constant, the result is nothing more than the familiar equations of constant acceleration.

• What tools and strategies would you use to carry out the calculations illustrated above?
• A similar model for the magnetic field around an inductor may be found here.
• Other recent electricity and magnetism visual puzzlers may be found here.