Electric charge is a basic property of matter that comes in two signs: positive (+) and negative (−). Electrons carry −e and protons +e (e ≈ 1.6×10⁻¹⁹ C). Like charges repel and opposite charges attract. For point charges the electrostatic force between two charges q₁ and q₂ separated by r is given by Coulomb’s law: |FE| = k|q₁q₂|/r² (k = 1/4πϵ₀). The force acts along the line connecting the charges; its direction depends on their signs. Electric permittivity (ϵ) of a medium tells you how the medium reduces the effective force compared to vacuum (ϵ₀). On the AP exam you’ll use these ideas to describe and calculate forces (CED allows up to 4 charges or high-symmetry cases) and compare electrostatic vs. gravitational forces. For a focused review, see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1), the Unit 10 overview (https://library.fiveable.me/ap-physics-2-revised/unit-10), and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Charge sign comes down to which elementary charge is in excess. Protons (in nuclei) each carry +e and electrons carry −e (CED 10.1.A.1.ii–iii). Normally objects are neutral because they have equal numbers of protons and electrons. If an object gains extra electrons it becomes negatively charged; if it loses electrons it becomes positively charged. Protons don’t move in ordinary materials, so charging usually happens by moving electrons (see Topic 10.2: the process of charging). The choice of “positive” vs “negative” is a historical convention, but the physics follows: Coulomb’s law (CED 10.1.A.2) tells you the force magnitude depends on |q1q2|/r^2 and the force direction depends on the signs (like charges repel, opposite attract, CED 10.1.A.3). For more on charging mechanisms and practice problems, check the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-10).

Coulomb’s law tells you how strong the electric force is between two point charges and which way it points. In simple terms: the force magnitude is proportional to the product of the two charges and falls off like 1/r^2 (inverse-square). Mathematically: |FE| = (1/4πε0) |q1 q2| / r^2 = k |q1 q2| / r^2. Same-sign charges repel; opposite-sign charges attract, and the force acts along the line joining them. Treat objects as point charges when their size is negligible (CED 10.1.A.1.iv). Use vector form and the superposition principle to add forces from multiple charges (CED boundary: up to four charges in AP problems). Remember ε0 is vacuum permittivity and appears when you need k = 1/(4πε0) (CED 10.1.C). This is a core AP 2 topic—practice calculating magnitudes, directions, and using superposition for up to four charges. For a quick review see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-10), and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Electric and gravitational forces are both inverse-square long-range forces, but they differ in key ways you need for AP Physics 2. Electric force (Coulomb’s law: FE = k|q1 q2|/r^2) can be attractive or repulsive depending on charge signs; gravitational force (Newton’s law: FG = G m1 m2 / r^2) is always attractive (CED 10.1.A.2, 10.1.B.1). For two charged masses, the electrostatic force is usually enormously larger than the gravitational force between them (CED 10.1.B.2), but gravity dominates at large (astronomical) scales because most large systems are electrically neutral (CED 10.1.B.3). Direction: electric force is along the line joining charges and set by sign (repel/attract); gravity is always toward the other mass. On the AP exam you may be asked to compare magnitudes, signs, or use Coulomb’s law vs Newton’s law in calculations—keep units and inverse-square dependence in mind. For extra review and practice problems on Topic 10.1, see the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and Unit 10 overview (https://library.fiveable.me/ap-physics-2-revised/unit-10).

Check the signs of the charges and use Coulomb’s law for the force’s magnitude and direction. If both charges have the same sign (both + or both −) they repel; if they have opposite signs (+ and −) they attract (CED 10.1.A.3.i–ii). For point charges the magnitude is |FE| = k |q1 q2| / r^2 and the force acts along the line joining them; the sign of q1q2 determines whether that line points toward the other charge (attraction) or away (repulsion) (CED 10.1.A.2–3). Remember: Coulomb’s law gives magnitude; use the charges’ signs to set direction. On the AP exam you’ll be expected to apply this (often with up to four charges and superposition) in Unit 10 problems. For a quick review, see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

When physicists say charge is quantized they mean any object's net electric charge comes in whole-number multiples of a single unit—you can't have 1.3 times that smallest unit. Mathematically: Q = n·e, where n is an integer and e is the elementary charge. The elementary charge e ≈ 1.602×10^−19 C. By the CED, an electron carries charge −e, a proton +e, and a neutron 0 (10.1.A.1.ii–iii). Coulomb’s law then uses these charges to find forces (10.1.A.2). For AP problems treat e as the indivisible unit (quarks have fractional charges but aren’t observed free in typical AP contexts). If you want more practice or a quick refresher on this topic, check the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-10), or try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

A point charge is just a simplifying model: you treat a charged object as if all its charge sits at a single point in space because the object's size is negligible compared to the distances you care about (CED 10.1.A.1.iv). That lets you use Coulomb’s law easily: FE = k|q1 q2|/r^2 with r the distance between the points and the force along the line joining them (10.1.A.2–3). Use the point-charge model when the separation between charges is much larger than the physical size of the objects (e.g., charged sphere looked at from far away). Remember the elementary charge e is the smallest indivisible charge (10.1.A.1.ii–iii). For multiple point charges, apply superposition: calculate each Coulomb force and add vectorially (CED keywords). AP exams expect you to use point-charge approximations in Coulomb’s-law problems (unit 10 practice items). For a quick refresher, see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1), the full unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-10), and tons of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Electric forces are enormously stronger than gravity for individual particles because the constants in the two laws differ hugely. Coulomb’s law uses k ≈ 9×10^9 N·m^2/C^2 while Newton’s gravity uses G ≈ 6.7×10^-11 N·m^2/kg^2, and for a proton and electron the electric attraction is about 10^39 times larger than their gravitational attraction. So at the particle level electric interactions dominate. We don’t notice that huge strength every day because ordinary matter is electrically neutral: positive charges (protons) and negative charges (electrons) cancel out at macroscopic scales, so net electric forces largely cancel while gravity always adds up (always attractive). Also charges in materials rearrange (polarization, conductors vs insulators) so local electric fields get screened. That’s why gravity, though weak, governs planets and stars while electric forces control atomic and molecular structure and contact forces (normal, friction) you experience (CED Topic 10.1, especially 10.1.A and 10.1.B). For a quick review, check the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

By Coulomb’s law (CED 10.1.A.2), the magnitude of the electrostatic force between two point charges is F = k|q1 q2|/r^2. If you double the separation r → 2r, the force changes by the factor 1/(2^2) = 1/4. So the force becomes one-quarter as large. The direction still depends on the signs of the charges: like charges repel, opposite charges attract (CED 10.1.A.3). On the AP exam you should be able to state and use this inverse-square dependence in calculations (the CED limits calculations to four or fewer charges). For a quick review, see the Topic 10.1 study guide on Fiveable (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to get comfortable applying the 1/r^2 relationship.

Permittivity shows up in Coulomb’s law and controls how strongly two charges interact. In vacuum the constant ε0 (≈ 8.85×10⁻¹² F/m) appears in the Coulomb constant k = 1/(4π ε0), so larger ε0 → smaller k → weaker force. In materials you use ε = κ ε0 (κ = relative permittivity or dielectric constant). A medium with κ > 1 becomes polarized by an external field, which reduces the effective field between charges and therefore reduces the magnitude of the Coulomb force by a factor of 1/κ compared to vacuum. Conductors and high-κ dielectrics polarize more easily; insulators polarize less. For AP Physics 2 you should be able to state this qualitative effect, use ε0 in Coulomb’s law, and relate relative permittivity (dielectric constant) to reduced force (Topic 10.1 and 10.1.C; see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1)). For extra practice, check the unit review (https://library.fiveable.me/ap-physics-2-revised/unit-10) and many practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Conductors (like metals) have lots of free charge carriers—electrons that can move easily through the material. That means when you put a conductor near other charges or an external field, those free electrons rearrange quickly, letting charge flow and cancel the internal electric field in electrostatic equilibrium. Insulators (like rubber or glass) have electrons tightly bound to atoms or molecules, so they can’t move freely from place to place. Instead, an external field only slightly shifts bound electrons relative to their nuclei (electric polarization), changing the material’s permittivity but not producing macroscopic charge flow. This distinction is exactly what Topic 10.1.C emphasizes: conductors allow easy movement of charge carriers; insulators do not. For more review, see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

In the static electricity lab you should’ve seen charged objects either attract or repel depending on sign—like two rubbed balloons repelling (both negative) or a rubbed balloon sticking to a neutral wall (induced polarization). You’d observe charging by friction (transfer of electrons), conduction (touching), and induction (bringing a charged rod near a conductor and grounding). Insulators hold localized charge; conductors let charge move. Small sparks or hair standing up show large local electric forces. These behaviors connect to Coulomb’s law (force ∝ |q1 q2|/r²) and the idea that direction depends on charge sign (CED 10.1.A.2–A.3). For exam prep, practice calculating forces (superposition, up to four point charges allowed) and think about permittivity/dielectrics if materials are involved. Review the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and try problems from Fiveable’s practice set (https://library.fiveable.me/practice/ap-physics-2-revised).

Use Coulomb’s law for each pair and the superposition principle: each other charge exerts a force F = k|q q0|/r^2 (k = 8.99×10^9 N·m^2/C^2) on the charge you care about. The steps: 1. For every other charge i, compute the magnitude Fi = k|qi q0|/r_i^2 and decide direction (repel if same sign, attract if opposite) along the line joining them (CED: 10.1.A.2–3). 2. Treat each Fi as a vector. If charges aren’t colinear, resolve each Fi into x and y components (Fx = Fi cosθ, Fy = Fi sinθ). 3. Sum components: Fnet,x = ΣFx_i, Fnet,y = ΣFy_i. 4. Get magnitude and direction: |Fnet| = sqrt(Fnet,x^2 + Fnet,y^2), θ = arctan(Fnet,y/Fnet,x). AP note: you’ll only be asked up to four interacting point charges except in high-symmetry cases (CED boundary). For worked examples and practice, see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and more practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

We use k in Coulomb’s law as a constant that sets the scale of the electrostatic force in SI units. Mathematically k = 1/(4πϵ0), where ϵ0 is the permittivity of free space. Its numeric value is about 8.99×10^9 N·m^2/C^2, so Coulomb’s law becomes |FE| = k |q1 q2|/r^2. Physically k (or ϵ0) tells you how easily electric field lines spread out in a medium: larger ϵ means field lines are “diluted” more and forces are weaker. In materials you replace ϵ0 with ϵ = κϵ0 (κ = dielectric constant), so the medium’s permittivity appears directly in the force. Remember the law is inverse-square and direction depends on the signs of charges (attract vs repel). For AP Physics 2 practice, see the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1) and hundreds of practice questions (https://library.fiveable.me/practice/ap-physics-2-revised).

Polarization means an external electric field shifts charges inside a material so opposite signs separate slightly—without adding net charge. In atoms or molecules electrons move a bit relative to positive nuclei (induced dipoles); in an insulator charges stay bound and just shift, while in a conductor free charges move and can pile up at surfaces. That local separation reduces the net field inside the material and is why materials have different electric permittivities (a measure of how easily they polarize). On the AP, this is covered in 10.1.C: electric polarization is modeled as induced rearrangement of electrons and helps explain dielectric behavior and why the permittivity of matter differs from ε0. If you want a short recap tied to the CED, check the Topic 10.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-2/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1), the full unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-10), and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to see polarization in capacitor/dielectric questions on the exam.