This applet demonstrates electrostatics 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 two positive charges. The yellow circle represents the charge; the white circles around it are equipotential lines (lines of constant potential). The field lines are also drawn in white. 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. Click on the objects, or the outer edge of the objects, to see what type they are.

Since this is a 2-D simulation, the electric field of charges is proportional to 1/r, like a line charge, not 1/r² like a point charge. It should be treated as a 2-D cross section, where all the charges and conductors extend in and out of the screen.

The Example 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:

• Double Charge: Two positive charges.
• Single Charge: A single positive charge.
• Dipole Charge: One positive and one negative charge.
• 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 by right-clicking on it and selecting "Edit". 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. The field varies linearly along the center line.

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 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 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/Potential: Show the electric field and the potential.
• Show E lines/Potential: Show the electric field lines and the potential.
• 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 Show Equipotentials checkbox draws equipotential lines, which are lines of constant potential.

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.

Click here to go to the applet.