Definition, with examples of electric field around a positive charge and a negative charge.

Finding the electric field due to more than one charge using the superposition principle, with the example of the electric field of a positive charge next to a negative charge.

Graphical representation of the electric field for an arrangement of a +3 charge next to a -1 charge, first using arrows and then using electric field lines. Definition and discussion of electric field lines.

Comparison between force due to gravity on earth and force on a charge in a uniform electric field. Electric field lines indicate direction of force on a charge, they are not trajectories.

The electric field for two charges with the same polarity, using the example of like charges with magnitudes 4 and 1.

Definition, including a representation of the electric field for a dipole. Atoms or molecules can become induced dipoles when placed in an electric field.

Using a charged rubber rod and two metal spheres to create a dipole. An electroscope is used to show that a dipole has been created.

Torque on a dipole in an electric field causes it to rotate and align with the field. Demonstration by creating a dipole and placing it in the electric field of a large Van de Graaff generator.

Demonstration of using grass seeds in oil to probe an electric field, with examples of the field for a dipole and for two charges of the same polarity.

Using a balloon to demonstrate the electric field between a Van de Graaff generator and an oppositely charged Professor Walter Lewin.

Calculating the electric flux through a surface by breaking it into small areas dA and integrating over the surface. Comparison between electric flux and air flow, with a diagram. Definition of a closed surface.

Definition, work required to bring charges from infinity into a specific arrangement. Conservative forces, just like gravity.

Definition, work per unit charge to move from infinity to a specific location. Measured in volts.

Finding the potential around an arrangement of multiple point charges, with examples of a pair of positive charges and a pair of charges with opposite polarity. Field lines are always parallel to equipotential surfaces, and equipotential surfaces with different potentials can never intersect.

Sometimes it is easier to work with potential difference rather than a complicated electric field. Distinction between potential V and potential energy U; do not confuse the two. Positive charges move from high to low potential energy, negative charges do the opposite.

Finding the difference in electric potential between two points A and B. Finding the change in kinetic energy from the potential difference. Any piece of metal is an equipotential surface, with example of a metal trash can attached to point A and a soda can attached to point B.

Potentials are generally defined relative to infinity, but often it doesn't matter where potential is defined to be zero because only the change in potential has any real meaning.

Using a large Van de Graaff generator and a fluorescent tube to show that there is a very large potential difference in a strong electric field.

Relationship between electric field and electric potential.

Field lines are perpendicular to equipotential surfaces. It takes no work to move charge perpendicular to the electric field. Comparison to contour lines on a ski mountain.

Finding potential from the components of the electric field. Gradient is defined.

Finding the electric field when potential is (10^5)*x in the x direction.

Finding the increase in kinetic energy when an electron is moved across a potential difference.

How changing potentials in heart cells keep the heart pumping.

Electrocardiograms, defibrillators, and pacemakers are explained, including a demonstration of an electrocardiogram on a student.

Description of scalar fields, with temperature as an example.

Illustrations of vector fields, using wind velocity as an example.

Uses gravity to describe the physics of a vector field.

Introduces electric fields by analogy to gravitational fields; introduces charge and electric force.

Introduces the superposition principle for electric force, shows an expression for electric field, and then applies the superposition principle to electric field.

Introduces electric potential energy and electric potential by analogy with gravitation; defines conservative forces and gives electric potential due to a point charge.

Introduces del operator and utilizes it to determine field from electric potential; in-class problem illustrates how to find electric field in 1D from plot of potential.

Derives an expression for the total electrostatic potential energy of a system of point charges.

Definition; field lines; fields for ring and disk of charge.

Historical context behind the developement of Field Theory, including differences with the "action at a distance" model.

Analytic representations of scalar fields and examples of visual representations: contour maps, color coding, and relief maps.

Definition of a vector; comparison of vector fields to scalar fields.

Utilizes gravity to illustrate the characteristics of a physical field.

Detailed discussion of the field line and iron filing or grass seed models of representing a vector field; introduction to time-varying field representation.

Electric field compared to gravitational field and defined, with a description of its field lines; superposition of electric field; force on charged particle due to electric field.

Definition of line, surface, and volume charge density in continuous charge distributions and calculation of the electric fields they produce.

Review of gravitational potential; introduction to electric potential by analogy to gravity; discussion of conservative forces and their relation to potential energy; introduction of the electronvolt.

Example determining the potential difference between two points in an electric field and illustrating that Coulomb forces are conservative.

Calculating electric potential due to discrete charges using superposition; includes configuration energy.

Description of how to derive the electric field from a potential; introduction of the del (∇) operator.

Introduction to charge and how it causes force via Coulomb's Law; description of resulting electromagnetic field.

Calculate the electric field and potential in a system of point charges, as well as the work required to bring in an additional point charge.

Solution (PDF)

Calculate the electric field and potential on the axis of a uniformly charged ring.

Solution (PDF)

Understand field line, flow field and grass seeds representations of vector fields.

What does a field line in the space surrounding a charge represent?

Given a field line drawing, determine whether the force between two particles is attractive or repulsive

Qualitatively describe the electric field produced by point charges.

Check understanding of electric potential landscape and potential energy, including correct signs for positive and negative charges.

Determine the direction electric field lines point within a potential landscape.

Understand magnitude and sign of electric field corresponding to plot of electric potential.

Plot vector fields in two dimensions given their mathematical expressions.

Solution (PDF)

Plot scalar fields in two dimensions given their mathematical expressions.

Solution (PDF)

Plot eight vector fields in two dimensions given their mathematical expressions.

Find mathematical expressions for vector fields with the specified magnitude and direction.

Determine the electric field at a point due to three point charges.

Determine the electric field and force in a square of four point charges.

Find the electric potential between two point charges.

Solution (PDF)

Conceptual questions about the relationships between electric field, electric potential, potential energy, and work.

Find the amount of work to assemble a system of point charges.

Find the electrostatic force, electric field and electric potential at the midpoint between two equal charges.

Find the work done and change in potential energy when two point charges are separated.

Calculating the electric potential along the axis and along the perpendicular bisector of a charged rod with given non-uniform charge density.

Use a given graph of electric potential to determine electric field and what kind of charge distribution caused it.

Solution (PDF)

Find the potential at a point due to a system of point charges; then, find the change in configuration energy of the system if another charge is brought to that point.

For a system of point charges, find the configuration energy of the system, the field, potential and force on a test charge at a given point, and the work needed to place that test charge.

3-part E-field problem; calculating and plotting E-field along x-axis.

Solution (PDF)

3-part Gauss's law problem; finding radial E-field and potential.

Solution (PDF)

6-part point charge problem; e-fields and potentials from point charge distribution; potential and kinetic energy.

Solution (PDF)

4-part voltage problem; finding radius and voltage of charged sphere.

Solution (PDF)

Finding position for third charge to cancel second; reaction to perturbation.

Solution (PDF)

Finding F and τ on dipole from E-field; charge of point from motion of dipole; acceleration from point charge force.

Solution (PDF)

Comparing potential and potential energy of opposite charges near a fixed point charge.

Solution (PDF)^#

Calculating initial speed of proton given distance traveled to nucleus.

Solution (PDF)^#

Explaining equipotentiality; comparing E-fields near spheres.

Solution (PDF)^#

4-part problem; finding force on one charge, E-field along x-axis and y-axis, graphing, and drawing field lines.

Solution (PDF)

Graphing and approximating electric potential; graphing potential energy.

Solution (PDF)

Finding field lines for E-field with given effect on dipole; F and τ on dipole for greater negative charge.

Solution (PDF)^#

For triangular arrangement of charges, finding the E-field, the force on a charge, and the motion of a charge.

Solution (PDF)^#