This applet is an electrostatics demonstration which displays the electric field in a number of situations. You can select from a number of fields and see how particles move in the field if it is treated as either a velocity field (where the particles move along the field lines) or an actual force field (where the particles move as if they were charged particles). This helps you visualize the field.

When you start the applet, you will see 500 particles moving in the "charged line" field, which is a field that attracts particles to the center. By default the particles are treating the field as a velocity field, which means that the field vectors determine how fast the particles are moving and in what direction. In this case, the particles just move toward the center and fall in. The velocity of all the particles at a certain point on the grid is always the same. If the field is treated as a force field, then the field vectors determine the acceleration of the particles, but their velocity may vary depending on where they started.

The Setup popup will allow you to select a vector field. The choices are:

• charged line: Charge evenly distributed along an infinitely long line through the center of the x-y plane.
• line charge double: Two charged lines.
• dipole lines: Two lines of opposite charge.
• quad lines: Two positive lines and two negative lines.
• point charge: This is the field of a single point of charge. This is a two-dimensional cross section of a three-dimensional field. In three dimensions, the divergence is zero except where the charge is located; but in this cross section, the divergence is positive everywhere (except at the origin, where it is negative).
• point charge double: Two point charges, with an adjustable separation between them.
• dipole: Two points with opposite charges, with an adjustable separation between them.
• quadrupole: Two positive charges and two negative charges.
• conducting plate: A conducting plate. The plate size is adjustable.
• charged plate: An evenly charged plate. The plate size is adjustable.
• charged plate pair: Two evenly charged plates. The size and separation of the two sheets are adjustable.
• charged plate dipole: Two evenly charged plates with opposite charges. The size and separation of the two sheets are adjustable.
• infinite plane: An infinite plane, evenly charged.
• conducting cylinder: A conducting cylinder with adjustable potential.
• cyl + line charge: A conducting cylinder near a line charge.
• cylinder in field: A grounded conducting cylinder in a uniform external field.
• dielec cyl in field: This is the electric field of a dielectric cylinder in a uniform external field. The size of the cylinder and the dielectric strength are adjustable.
• slotted conducting plane: This is a grounded conducting plane with a rectangular slot cut in it. The plane is placed in a uniform external field. The width of the slot is adjustable.
• conducting planes w/ gap: Two infinite conducting planes, one at positive potential and one at negative potential, with a gap between them.

The Color popup will allow you to select what the color of the floor means. Generally the floor color will indicate the value of some quantity at that point, where green means positive, gray means zero, and red means negative. Here are the possibilities:

• Field Magnitude means the floor indicates the strength of the field. It will be green if the field is strong and gray if it is weak or not present.
• Potential means the floor indicates the value of the potential function, if any.
• None means the floor is gray.
• Charge means the floor indicates the divergence of the field, which is equal to the charge density.

The Floor popup allows you to select whether grid lines, equipotentials, or field lines are drawn on the floor, or none of the above.

The Flat View checkbox allows you to select a two-dimensional view of the vector field rather than showing the particles on a potential surface. This is done automatically when viewing field vectors or when taking a line or surface integral.

The Display popup will allow you to select how the particles will move:

• Display: Particles (Vel.) means particles will move through the field, with the field vectors determining their velocity.
• Display: Particles (Force) means particles will move through the field, and the field vectors determine their acceleration.
• Display: Field Vectors shows you the field vectors at an array of locations.
• Display: None doesn't show any particles or field vectors.

The Mouse popup controls what happens when you click on the view. If you set it to Adjust Angle or Adjust Zoom, you can adjust the orientation or size of the 3-d view by clicking and dragging.

If you select Line Integral from the mouse popup, you can perform a line integral by clicking and dragging out a rectangular area. This will show the circulation around that area. It should be zero, by Faraday's law, since this is a static field.

If you select Surface Integral from the mouse popup, you can perform a surface integral by clicking and dragging out a rectangular area. This will show the flux through the bounds of that area. It should be proportional to the total charge inside, by Gauss's Law.

The Stopped checkbox will stop the particles.

The Reverse checkbox will reverse the direction of all the field vectors.

The Reset button can be used to reset the positions of all the particles to random values.

The Kick button can be used to give all the particles a random acceleration in some direction. This is only allowed if the particle movement is set to "Force". It can be useful if none of the particles are moving, or if they are all moving in the same direction.

The Field Strength slider makes the field stronger or weaker, and also adjusts the brightness of the field vectors if you have Display: Field Vectors selected.

The Vector Density slider controls the number of vectors present if you have Display: Field Vectors selected.

The Number of Particles slider allows you to reduce the number of particles, which can be useful if you want to watch the behavior of just a few of them. Also it might speed things up if you have fewer particles.

A few additional field-specific sliders may be present, depending on the field you have selected.

Click here to go to the applet.