Click here to go to the applet.
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
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
- 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
- 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 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
- Dielectric Cyl + Field: A dielectric cylinder in an external
- 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
- 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
- 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.
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