Unit 10 · Electric Force, Field, and Potential

Electric charge ● (core concept) — A fundamental property of all matter, described as positive or negative. Like signs repel, opposite signs attract, with the force directed along the line joining the charges.

Elementary charge ● (core concept) — e = 1.60×10⁻¹⁹ C, the magnitude of the charge of a single electron or proton; treated as the smallest indivisible unit of charge. Electrons carry −e, protons +e, neutrons carry no charge.

Point charge ● (core concept) — A model in which a charged object's physical size is negligible in the situation being analyzed, so the object can be treated as a single point of charge.

Coulomb's law ● (core concept) — |F_E| = k|q₁q₂|/r² = (1/4πε₀)|q₁q₂|/r²: the electrostatic force between two charges is proportional to each charge's magnitude and inversely proportional to the square of the separation. Direction: repulsive for like signs, attractive for opposite signs, along the line between them.

Coulomb constant ● (core concept) — k = 1/(4πε₀) = 9.0×10⁹ N·m²/C², the proportionality constant in Coulomb's law. ε₀ = 8.85×10⁻¹² C²/(N·m²) is the vacuum permittivity.

Electrostatic vs. gravitational force ● (core concept) — Electrostatic forces can attract or repel, while gravity is always attractive. For two charged massive objects the electrostatic force is usually far larger — yet gravity dominates at large scales because large-scale systems are electrically neutral.

Electric permittivity ● (core concept) — A measure of how readily a material or medium polarizes in an electric field. Free space has the constant value ε₀; matter has a different value set by its composition and the ease with which its electrons rearrange.

Electric polarization ● (core concept) — The induced rearrangement of electrons by an external electric field, separating positive and negative charges within a material or medium.

Conductor vs. insulator ● (core concept) — Conductors are made of materials whose charge carriers move easily; insulators are made of nonconducting materials whose charge carriers cannot move easily.

Charge carrier ● (core concept) — A particle that carries electric charge through a material — electrons in metal conductors, ions in electrolytes. Current is the collective motion of charge carriers.

Conservation of electric charge ● (core concept) — A system's net charge stays constant unless charge is transferred to or from it. Charging a system (by friction or contact) moves electrons into or out of the system; the total charge of system plus surroundings never changes.

Induced charge separation ● (core concept) — When the electrostatic force from a nearby charged system redistributes the charges inside another system — polarizing it — without any net charge transfer. It can occur in neutral systems and underlies charging by induction.

Grounding ● (core concept) — Electrically connecting a charged system to a much larger, approximately neutral system (e.g., Earth), allowing charge to flow until the system's net charge is neutralized.

Charging by friction or contact ● (core concept) — Charging a system requires transferring electrons into or out of it — by rubbing (friction) or by touching a charged object to it (contact). The process conserves total charge: one system gains what the other loses.

Electric field ● (core concept) — E = F_E/q: the electric force per unit charge at a point, measured using a small test charge that does not disturb the field. A vector; it points away from isolated positive charges and toward isolated negative charges, and the force on a positive test charge points in the field's direction.

Electric field of a point charge ● (core concept) — |E| = k|q|/r²: the field strength a distance r from a point charge of magnitude |q|, directed radially outward (positive q) or inward (negative q). The net field from several charges is the vector sum of the individual fields.

Electric field line diagrams ○ — Simplified models of vector field maps showing the relative magnitude (line density) and direction of the electric field. Lines start on positive charges and end on negative charges (or infinity).

Electrostatic equilibrium (conductor) ● (core concept) — In electrostatic equilibrium, a solid conductor's excess charge sits on its surface and the electric field inside the conductor is zero. At the surface the field is perpendicular to the surface.

Electric field of a charged sphere ● (core concept) — Outside an isolated sphere with a spherically symmetric charge distribution, the field is the same as that of a point charge carrying the sphere's net charge, located at the sphere's center.

Electric field inside an insulator ● (core concept) — Excess charge on an insulator in electrostatic equilibrium is distributed through its interior and on its surface, so the field inside can be nonzero. AP Physics 2 treats insulator fields only qualitatively.

Test charge ● (core concept) — A small positive charge used to probe an electric field. It must be small enough not to disturb the charges creating the field; by convention the field direction is the direction of the force on a positive test charge.

Electric potential energy (two charges) ● (core concept) — U_E = kq₁q₂/r: the work an external force must do to bring two point charges from infinitely far away to their current separation. Positive for like charges, negative for opposite charges.

Total electric potential energy ● (core concept) — The sum of kq_iq_j/r_ij over every distinct pair of charges in the system. AP Physics 2 calculates this only for configurations of four or fewer point charges.

Electric potential ● (core concept) — V = U_E/q: the electric potential energy per unit charge at a point in space. A scalar; potential difference, not absolute potential, is what drives charge motion.

Electric potential of point charges ● (core concept) — V = kΣ(q_i/r_i): the potential at a point is the scalar sum of each point charge's contribution. Calculations are limited to four or fewer particles (more allowed only in high symmetry). Potential is taken as zero at infinity from an isolated point charge.

Electric potential difference ● (core concept) — ΔV = ΔU_E/q: the change in electric potential energy per unit charge when a test charge moves between two points. Batteries create potential difference by chemical processes that separate positive and negative charges.

Field from potential difference ● (core concept) — |E| = |ΔV/Δr|: the average electric field between two points equals the potential difference divided by their separation (for a uniform field). The field vector points in the direction of decreasing potential.

Equipotential lines ● (core concept) — Lines of equal electric potential (isolines). They are everywhere perpendicular to electric field vectors, and there is no field component along an isoline.

Conductors in contact (same potential) ● (core concept) — When conductors are in electrical contact, electrons redistribute so that the conductors' surfaces are all at the same electric potential.

Capacitor (parallel-plate) ● (core concept) — Two separated parallel conducting plates that hold equal and opposite charge ±Q. AP Physics 2 analyzes only parallel-plate capacitors and ignores edge effects.

Capacitance ● (core concept) — C = Q/ΔV: the magnitude of charge stored per plate divided by the potential difference the separated charge creates. Depends only on the capacitor's geometry and the material between the plates.

Parallel-plate capacitance ● (core concept) — C = κε₀A/d: proportional to plate area A, inversely proportional to plate separation d, with κ the dielectric constant of the material between the plates (κ = 1.0 for air).

Electric field between capacitor plates ● (core concept) — Uniform in magnitude and direction between the plates (except near edges): E = Q/(κε₀A), directed from the positive plate to the negative plate. A charged particle between the plates accelerates uniformly, like a projectile in Earth's gravity.

Energy stored in a capacitor ● (core concept) — U_C = (1/2)QΔV: the electric potential energy stored equals the work an external force did to separate the charge onto the plates.

Dielectric ● (core concept) — An insulating material placed between capacitor plates. It raises the capacitance and sets up an induced electric field opposing the plates' field.

Dielectric constant ● (core concept) — κ: a dimensionless number characterizing the insulating material between capacitor plates (κ = 1.0 for air). Larger κ means larger capacitance for the same geometry.

Charge moving through a potential difference ● (core concept) — ΔU_E = qΔV: when a charged object moves between two potentials, its electric potential energy changes by qΔV. The lost or gained potential energy becomes kinetic energy of the object, consistent with conservation of energy.