Visualizing {+2-1} Charge Triplets for UM-StL Physics 112

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  • This release dated 1 Mar 1996 (Copyright by Phil Fraundorf 1988-1996)
  • At UM-StLouis see also: cme, infophys, physics&astronomy, programs, stei-lab, & wuzzlers.
  • Accel-1D pages: derivations, slow-example, fast-example&twins, x-tv Plots, x-ct Plots, 4-vectors, rap.
    Electric Potential and Field Magnitude around a {+2-1} Equilateral Triplet
    Here we've used 1 [coulomb] charges separated by 1 [meter]. The peaks are truncated because the Mathematica software with which these were generated chooses scale maxima and minima for such plots by default automatically. Below left: The electric potential is in [volts] or [joules per coulomb]. Below right: The electric field magnitude is in [volts per meter] or [newtons per coulomb].

    Electric Potential and Field Magnitude w/EquipPotential Lines & Field Arrows
    Below left: Note that field arrows are always perpendicular to the equipotential lines in their vicinity. Below right: Note the field magnitude MINIMUM between the two positive charges. The field magnitude also decreases between unlike adjacent pairs, but not nearly as much.
    Note: Crazy colors and bright red are "OFF SCALE" regions in the plot. Otherwise, colors run from orange (MIN), through yellow, green, cyan, and blue, up to magenta (MAX). To figure what MIN and MAX mean, you may need to look at the 3D plots at the top.

    Field Azimuthal Angle Phi w/Equipotential Lines & Field Arrows
    Note that Phi=0 or 360 degrees (red) points to the left, while the other colors correlate with different directions for the field arrows superposed on the image.

    Field x and y Components w/Equipotential Lines & Field Arrows
    Are these cool colors, or what? This "dipole appearance" of a spherically symmetric field around a point is actually seen when imaging mechanical strain, as distinct from electrostatic, fields around spherical inclusions using "darkfield" diffraction contrast in a transmission electron microscope. This is because choosing the reflection forming the image effectively chooses the field component which gives rise to intensity in the image! Thus an electron microscopist might see the two images below as micrographs of the same three defects (two extrinsic and one intrinsic) formed using electrons which have been "Bragg reflected" to the left, and up, respectively. For more on this cf. Electron Microscopy of Thin Crystals by Hirsch et. al. (1967).

    Visualizing some other possible exam problems: DiPole, DiWire.