This java applet demonstrates electrostatics and static current distributions in two dimensions. There is also a three dimensional applet which is more accurate but less flexible.

When the applet starts up you will see the electric field of a single positive charge. The yellow circle represents the charge; the white circles around it are equipotential lines (lines of constant potential). The green arrows indicate the electric field. The charge can be dragged around the screen with the mouse.

In general, yellow represents positive charge, and blue represents negative charge.

Conductors, dielectrics, and media with bound charges will show up as gray. There aren't enough colors or shades of gray to make the different kinds of media look different. Use the Show Material Type menu option to tell them apart.

The Setup popup can be used to view some interesting pre-defined experiments. Once an experiment is selected, you may modify it all you want. The choices are:

• Single Charge: this is a single positive charge.
• Double Charge: Two positive charges.
• Dipole Charge: One positive and one negative charge. The equipotential between the two charges should be a straight line; set the accuracy menu to a higher setting to make it straighter.
• Charge + Plane: A charge near a grounded conductor. Note that the field in the upper half is nearly the same as in Dipole Charge (it should be exactly the same). The blue color on the conductor indicates negative surface charge, which is put there to balance the external field and maintain the conductor at ground.
• Dipole + Uniform: A dipole in a uniform field.
• Quadrupole Charge: Two positive and two negative charges.
• Conducting Planes: Two conductors fixed at opposite potentials. The yellow and blue color on the outer edge of the conductors indicate positive and negative surface charges. Charge is added to or removed from each conductor as needed to maintain the potential.
• Charged Planes: Two uniformly charged planes.
• Conducting Cylinder: A cross section of a conducting cylinder at positive potential.
• Grounded Cyl + Charge: A cross section of a grounded conducting cylinder with a charge next to it.
• Grounded Cyl + Field: A cross section of a grounded conducting cylinder in a uniform field.
• Charged Cylinder: A cross section of an uniformly charged cylinder.
• Charged Hollow Cyl 1: A cross section of an uniformly charged hollow cylinder. Note that there is no field in the cavity, since the potential is constant there.
• Charged Hollow Cyl 2: A cross section of an uniformly charged cylinder with an off-center cylindrical cavity inside. Note that there is a uniform field in the cavity.
• Floating Cyl + Charge: A cross section of a cylinder with floating potential, with a charge next to it. The charge on the cylinder is a constant (zero), so the potential will vary depending on where the charge is. If the charge is deleted then the cylinder will be at ground.
• Floating Cyl + Plates: A cross section of a cylinder with floating potential, with two plates at positive and negative potentials. The charge on the cylinder is a constant as long as it is not touching anything, so the potential will vary depending on where it is located. If you move the cylinder so it is touching one of the plates, then enough charge will move onto the cylinder to make its potential the same as the plate it is touching.
• Conducting Box: A conducting box at positive potential. The field is zero inside, since the potential is constant. Note that the field is stronger at the corners.
• Sharp Point: A conductor at positive potential, coming to a sharp point. Note that the field is strongest at the point.
• Corner: The corner of a conductor at positive potential.
• 45 Degrees: A 45 degree corner of a conductor at positive potential. The field near this corner is stronger than the field near a 90 degree corner.
• 135 Degrees: A 135 degree corner of a conductor at positive potential. The field is weaker than near a 90 degree corner.
• Dielectric Cylinder: A dielectric cylinder with a charge near it.
• Dielectric Cyl + Field: A dielectric cylinder in an external uniform field.
• Dielectric 1: A charge near a dielectric boundary. Notice that the field lines bend toward the boundary.
• Dielectric 2: A charge inside a dielectric, near the boundary. Notice that the field lines bend away from the boundary.
• Dielectric + Dipole: A dipole with a dielectric boundary between the charges.
• Dielectric Capacitor: Two conducting planes at opposite potentials with a dielectric between them. The surface charge on the planes is stronger at the dielectric boundary. You can see the total charge on each plane by moving the mouse over one of them; the charge is shown in the lower-left hand corner of the screen. The dielectric strength can be adjusted using the Mouse = Adjust Dielectric menu option, by dragging out an area including the dielectric with the mouse and then fiddling with the Dielectric Constant Slider. This will affect the amount of charge on each plane. The stronger the dielectric, the more charge on each plane, and the higher the capacitance between the two planes.
• Conducting Planes w/ Gap: Two conducting planes at opposite potentials with a gap between them.
• Slotted Conducting Plane: Two grounded conducting planes with a gap between them, in an external field. Some of the field leaks through the gap.
• Shielding 1: A grounded conducting box shielding its interior from an external uniform field.
• Shielding 2: A grounded conducting box shielding its exterior from a charge inside.
• Box w/ One Live Side: A grounded conducting box with one side that is at positive potential.
• Quadrupole Lens: This is an electrostatic quadrupole lens, used to focus particle beams. It is similar to the magnetic quadrupole lens used in particle accelerators. It consists of four hyperbola-shaped conductors at alternating potentials.
• Wire w/ Current: This is a wire carrying current from the top of the screen to the bottom. The current is indicated by the yellow arrows. Since the wire has resistance, the potential drops continuously over the length of the wire.
• Resistor: This is two wires connected to a resistor, all carrying current. The potential drops continuously over the length of the resistor, and less so over the length of the wire (since its resistance is lower). Since the electric field is stronger in the resistor than in the wire, there is some charge at the top and bottom of the resistor to maintain this discontinuity in the field. This charge causes the resistor to have some stray capacitance.
• Resistors in Parallel: This shows three resistors in parallel. The middle one has the highest resistance, so the current is weakest there. The left one has the lowest resistance.
• Current in 2D 1: This shows the flow of current in a two-dimensional plate.
• Current in 2D 2: This shows the flow of current in a wire which is wider in the middle.

The Mouse popup controls what happens when the mouse is clicked. The following settings are possible:

• Mouse = Move Object: Clicking on an object (a conductor, draggable charge, area of bound charge, or dielectric) will allow you to drag it somewhere else on the screen. Objects that extend offscreen cannot be moved.
• Mouse = Delete Object: Clicking on an object (a conductor, draggable charge, area of bound charge, or dielectric) will delete it.
• Mouse = Add + Draggable Charge: Clicking on a point will create a positive draggable charge there.
• Mouse = Add - Draggable Charge: Clicking on a point will create a negative draggable charge there.
• Mouse = Clear Square: Clicking on a square will remove whatever is there (conductor, bound charge, dielectric). This will remove just one square, as opposed to Delete Object which will delete all connected squares. This won't remove draggable charges; use Delete Object to remove those.
• Mouse = Add Conductor (Gnd): Clicking on a point will create a conductor fixed at ground.
• Mouse = Add + Conductor: Clicking on a point will create a conductor fixed at positive potential.
• Mouse = Add - Conductor: Clicking on a point will create a conductor fixed at negative potential.
• Mouse = Add + Charge Square: Clicking on a point will create a square of positive bound charge.
• Mouse = Add - Charge Square: Clicking on a point will create a square of negative bound charge.
• Mouse = Add Dielectric: Clicking on a point will create a square of dielectric medium.
• Mouse = Make Floater: Clicking on a conductor will cause it to have a floating potential. Most conductors in this applet are at fixed potential, which means that charge is added or removed as needed to maintain a constant potential. A floating conductor has a constant charge, so the potential will vary depending on what charges are nearby. Only one conductor on the screen can be floating. If you make any changes to a floating conductor then it will be changed into an ordinary conductor; you will have to use Make Floater to make it floating again.
• Mouse = Adjust Conductivity: Clicking on a point and dragging out a rectangular area will allow you to adjust the conductivity of the conductors in that area using the Conductivity slider. The Show Material Type menu option may come in handy here (and in the following options) to see feedback from the changes you are making and to compare the conductivity of all conductors on the screen.
• Mouse = Adjust Dielectric: Clicking on a point and dragging out a rectangular area will allow you to adjust the dielectric constant on the dielectrics in that area using the Dielectric Constant slider.
• Mouse = Adjust Potential: Clicking on a point and dragging out a rectangular area will allow you to adjust the potential on the conductors in that area using the Potential slider. This can also be used to change the potential of a floating conductor.
• Mouse = Adjust Charge: Clicking on a point and dragging out a rectangular area will allow you to adjust the charge on the draggable or bound charges in that area using the Charge slider.

The Show popup determines which fields or other quantities to display, and how to display them.

• Show Electric Field (E): Show the electric field as arrows. The arrows go from dark green to light green and then to white as the field gets stronger.
• Show E Lines: Show the electric field as lines. The color of the lines go from dark green to light green and then to white as the field gets stronger. The density of the lines is kept fairly constant, so in order to determine the field strength you need to look at the color of the lines rather than how far apart they are.
• Show Potential (Phi): Show the potential; green is positive, red is negative, and black is ground.
• Show Vector Potential: Show the vector potential (A) as arrows.
• Show Magnetic Field (B): Show the magnetic field as green (positive, toward you) or red (negative, away from you).
• Show Current (j): Show the current density as yellow arrows.
• Show Charge (rho): Show the charge density as yellow (positive) or blue (negative).
• Show Displacement (D): Show the electric displacement vector.
• Show Polarization (P): Show the electric polarization vector.
• Show Polarization Charge: Show the polarization charge density.
• Show Material Type: Since all materials show up as gray, you need this option to tell them apart:
  • Conductors: cyan () (lighter shades indicate better conductors)
  • Floating Potential Conductors: purple ()
  • Dielectrics: orange () (lighter shades indicate stronger dielectrics)
  • Bound Charges: blue () or yellow ()
• Show rho/j: Show both the charge density and the current.
• Show E/rho: Show both the electric field and the charge density.
• Show E lines/rho: Show both the electric field lines and the charge density.
• Show E/j: Show the current density in conductors and the electric field outside of conductors.
• Show E lines/j: Show the current density in conductors and the electric field lines outside of conductors.
• Show E/rho/j: Show the current density in conductors and the electric field outside of conductors. Also, show the charge density.
• Show E lines/rho/j: Show the current density in conductors and the electric field lines outside of conductors. Also, show the charge density.
• Show E/phi: Show the electric field and the potential.
• Show E lines/phi: Show the electric field lines and the potential.
• Show E/Phi in conductors: Show the electric field, and in conductors also show the potential.
• Show E lines/Phi in conductors: Show the electric field lines, and in conductors also show the potential.
• Show E/Phi/j: Show the current density in conductors and the electric field outside of conductors. Also show the potential.
• Show E lines/Phi/j: Show the current density in conductors and the electric field lines outside of conductors. Also show the potential.
• Show B/j: Show the magnetic field and the current density.
• Show E/B/rho/j: Show the electric and magnetic field outside of conductors and the charge and current densities inside.
• Show E lines/B/rho/j: Show the electric field lines and magnetic field outside of conductors and the charge and current densities inside.
• Show Ex: Show the X component of the electric field.
• Show Ey: Show the Y component of the electric field.
• Show Dx: Show the X component of the electric displacement.
• Show Dy: Show the Y component of the electric displacement.

The Accuracy popup controls the accuracy used to calculate the fields. Lower accuracy is faster but may display misleading or incorrect results.

The Clear All button clears the screen.

The Stop Calculation checkbox stops the calculation of the fields. You can check this temporarily if you want to make a bunch of changes without having the calculation slow you down. Then when you're done, uncheck it to have the fields calculated.

The Enable Current checkbox allows current to flow. When this is checked, the top of the screen is fixed at positive potential and the bottom of the screen is fixed at negative potential. If there is a conducting path from the top to the bottom of the screen, then current will flow. Any conductors not connected to the top or bottom of the screen will be at ground.

The Draw Equipotentials checkbox draws equipotential lines, which are lines of constant potential.

The Resolution slider allows you to speed up or slow down the applet by adjusting the resolution; a higher resolution is slower but looks better.

The Brightness slider controls the brightness, just like on a TV set. Also when the brightness is higher it causes more equipotentials to be drawn.

The Equipotential Count slider allows you to control the number of equipotentials independently from the brightness.

This is obviously not correct; it's not possible to have steady-state current flow into a dead end. The problem is that the branch has a very thin separation between it and a conductor at higher potential, and that confuses the applet.

To fix this, either use a higher accuracy setting (which will be slower) or make the separation wider, like so:

Click here to go to the applet.