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.

Definition, with link to a visualization.

Comparison of gravitational and electric fields. Electric field lines defined with diagrams. Example problem without solution.

Potential and potential energy for electrostatics compared to same concepts for gravity. Volt is defined as the unit for potential difference. Potential landscapes illustrated by diagram. Equation for potential created by a point charge.

Derivation of electric field as the gradient of potential

Energy required to bring charges from infinity into a specific arrangement. Examples for 2 and 3 point charges.

Relationship between electric field and electric potential for point charges.

Finding electric potential using electric fields calculated from Gauss's Law. Worked example with diagrams of a nonconducting sphere of uniform charge.

Electric potential; Lorentz force and magnetic force; Biot-Savart Law; magnetic dipole moments

Finding the electric field, electric potential, magnetic field, and field energy between the plates of a charging capacitor.

Scalar fields and vector fields are defined, with diagrams and examples. Brief review of gravitational field and introduction to electric field, with important equations for each.

Definitions, with equations. Superposition, charge densities, and unit vectors are also defined.

Definitions, with equations and properties.

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

Showing fields through arrows, field lines, grass seeds, and iron filings; motion of fields.

Definition; fields for point charges and field lines; force from fields.

Definition; gravitational work and conservative forces; potential and potential energy for gravity.

Defined for E-fields and calculated for point charges and continuous distributions.

Deriving E-field from potential; equipotential surfaces defined.

Question about the electric field for two unequal point charges with opposite signs, with answer and explanation.

Two questions with answers and explanations.

Two questions with answers and explanations.

Question about electric field of a dipole, with answer and explanation. Question about force on a dipole in an electric field, with answer and explanation.

Question with answer and explanation.

Five questions with answers and explanations.

Two questions about determining the electric field when the electric potential is known, with answers and explanations.

Question about walking down a mountain most quickly, with answer and explanation.

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)^#