Calculating the electric field between two planes with uniform but opposite charges. Diagram of the end effects for the electric field around finite planes of charge.

Van de Graaff generator and a large metallic plane used to show that the electric field for a plane falls off much more slowly than the electric field of a sphere of charge.

Metallic ping pong balls and a hollow conducting sphere used to show the the electric field inside a uniformly charged sphere is zero.

A metallic ping pong ball and two charged plates used to show that the electric field between two plates is much stronger than the field around the plates.

Finding the potential inside and outside of a positively charged hollow sphere. Equipotential surfaces are defined, and compared to contour lines on a map.

Scalar and vector fields, with visual examples. Source, sink, and circulating fluid flow as a vector field, with links to visualizations. Vector field diagrams and field lines, with example of gravitational vector field.

Definition, including link to a visualization and mention of the dipole moment.

Electric fields created by dipoles, including the point dipole approximation and a link to a visualization.

Behavior of dipoles in uniform electric fields, including the torque on the dipole and a link to a visualization.

Method for finding the electric field of charge distributions, including definition of charge density for volume, area, and length. Links to visualizations for finding the electric field of an infinite line of charge and for a ring of charge. Step-by-step calculation of the electric field of a ring of charge. Examples of electric field for a finite line of charge and a disk of charge, with limits of each. Summary of E fields for dipoles, point charges, lines of charge, and planes of charge.

Superposition and charge densities defined, with general equation for calculating electric field due to a continuous charge distribution.

Definition; e-field of dipole and motion of dipole in E-field; potential energy of dipole.

Volume, surface, and line charge densities defined; e-fields from rods, rings, disks, and planes.

Strategies and solved E-field problems: Hydrogen atom; Millikan oil drop; motion perpendicular to E-field; e-fields of dipoles, arcs, and finite rods.

Potential calculated for rods, rings, and disks; e-field from potential.

Strategies and solved potential problems: Two charges, dipole, annulus, charged wire.

Strategies and solved Gauss's Law problems: Parallel planes; flux through flat surface; gravity; potential of sphere.

Creating and destroying E-fields by creating or destroying dipoles.

5-part E-field problem; calculating and plotting E-field along z-axis; limiting cases; connection to Coulomb's law.

Solution (PDF)

Drawing and explaining electric field near ellipsoid conductor.

Solution (PDF)

4-part problem; finding charge distribution, electric field, and potential for charged cylinder, then again with a dielectric.

Solution (PDF)

3-part problem; finding E-field above, below, and within a slab of charge with an opposite sheet of charge on top.

Solution (PDF)

Finding and sketching E-field, potential, and potential energy.

Solution (PDF)^#

5-part problem; finding charge, potential energy, and electric potential.

Solution (PDF)^#

Interactive applet showing the magnitude and direction of the electric field around a dipole.

Applet demonstrating the method of integrating to find the electric field at a point above a line of charge.

Interactive applet showing the magnitude and direction of the electric field due to a finite line of charge.

Applet demonstrating the method of integrating to find the electric field at a point above a ring of charge.

Interactive applet showing the magnitude and direction of the electric field due to a ring of charge.

Video demonstration of the force on a charge in an electric field that changes over time.

Video demonstrating the creation of an electric dipole by separating a positive and negative charge which were originally in the same spot.

Video showing the creation of a dipole electric field by moving 5 positive charges away from 5 negative charges one-by-one.

Video showing the destruction of a dipole electric field by moving the positive charges of the dipole toward the negative charges.

Applet simulating the interaction of large numbers of dipoles in a two-dimensional space.

Interactive applet which simulates the behavior of charged particles in a potential well.

Video demonstrating the formation of an atom from a positive nucleus attracting four electrons.

Applet simulating a series of oppositely charged particles attached to two fixed endpoints, sagging under the weight of gravity. Neutral charges can be dropped onto this arrangement to weigh it down further.

Applet simulating a lattice of positive and negative particles attached to four fixed corners, sagging under the weight of gravity. Neutral charges can be dropped onto this arrangement to weigh it down further.