Electrostatics in AP Physics 2: Forces, Fields, and Electric Potential

Electric charge

A fundamental property of matter that determines how an object participates in electric interactions.

Charge interaction rules

Like charges repel; opposite charges attract.

Conservation of charge

In an isolated system, net charge remains constant; charge can be transferred but not created or destroyed.

Electrostatics

The study of electric charges at rest and the forces/fields they produce (not sustained electric currents).

Electron transfer (charging by electrons)

Objects typically become charged by moving electrons: gaining electrons makes an object negative; losing electrons makes it positive.

Charging by contact (conduction)

Charge transfer by touching (or through a conducting path), causing charge to redistribute between objects.

Charging by induction

Charging without contact: a nearby charge causes charge separation; with grounding, a net charge can remain after the inducer is removed.

Grounding

Connecting to Earth (a large charge reservoir) so electrons can flow into or out of an object.

Quantization of charge

Net charge comes in discrete amounts rather than any continuous value.

Elementary charge (e)

The magnitude of the charge of an electron/proton: e = 1.60 × 10⁻¹⁹ C.

Charge quantization equation (q = ne)

Any net charge q is an integer multiple of e, where n is an integer (positive, negative, or zero).

Coulomb’s law

Magnitude of electric force between point charges: F = k|q₁q₂|/r².

Coulomb’s constant (k)

k = 8.99 × 10⁹ N·m²/C².

Point charge approximation

Treating a charge distribution as concentrated at a point (valid for point charges or spherically symmetric objects observed from outside).

Inverse-square dependence

For point charges, force and field magnitudes scale as 1/r² with distance r.

Newton’s third law (electrostatics)

Two charges exert equal-magnitude, opposite-direction forces on each other.

Superposition principle (electric effects)

Net force or net electric field equals the vector sum of contributions from each source charge considered independently.

Vector addition via components

In 2D problems, resolve each force/field into x and y components, add components, then recombine for magnitude/direction.

Electric field (concept)

A vector “influence map” created by source charges; it determines the force on any charge placed at a point.

Electric field definition (E = F/q)

Electric field at a point is force per unit positive test charge: ⃗E = ⃗F/q (q is a small positive test charge).

Force from an electric field (F = qE)

A charge q in a field experiences ⃗F = q⃗E; negative charges feel force opposite the field direction.

Electric field from a point charge (magnitude)

At distance r from point charge Q: E = k|Q|/r².

Electric field direction (point charge)

Field points away from a positive source charge and toward a negative source charge.

Electric field lines

A visual model representing electric field direction and relative strength; field lines are not physical objects.

Field lines start/end rule

Field lines start on positive charges and end on negative charges (or at infinity if there is net charge).

Field lines never cross

Electric field lines cannot intersect because the field cannot have two different directions at one point.

Field-line density meaning

Where field lines are closer together, the electric field magnitude |E| is larger.

Conductor

A material in which charge (typically electrons) can move freely through the material (e.g., metals).

Insulator

A material in which charge is not free to move throughout; excess charge tends to remain localized near where it is placed.

Polarization

Induced separation of charge within a neutral object, producing a negative side and a positive side without changing net charge.

Electrostatic equilibrium

The state in a conductor when charges are no longer moving (static situation).

E = 0 inside a conductor (equilibrium)

In electrostatic equilibrium, the electric field inside a conductor is zero; otherwise charges would move.

Excess charge on a conductor’s surface

In electrostatic equilibrium, any net (excess) charge on a conductor resides on its outer surface.

Constant potential in a conductor

In electrostatic equilibrium, electric potential is the same everywhere inside a conductor and on its surface.

Charge concentration at sharp points & lightning rods

Charge density is higher at regions of sharper curvature, producing stronger local fields; lightning rods use sharp tips to enhance field and promote charge leakage.

Faraday cage

A conducting enclosure that shields its interior from external static electric fields because charges redistribute to make the interior field zero.

Conservative electric force

Electrostatic forces are conservative: work done by the electric field depends only on initial and final positions, not the path.

Electric potential energy (two point charges)

System potential energy (zero at infinity): U = k(q₁q₂)/r. U>0 for like charges; U<0 for opposite charges.

Electrostatic work–energy relation

If only electrostatic forces do work: ΔK + ΔU = 0 (mechanical energy is conserved).

External work in quasistatic motion

If an external agent moves a charge slowly so ΔK≈0, then W_ext = ΔU.

Work done by the electric field

Work by the field is the negative of the potential energy change: W_field = −ΔU.

Electric potential (voltage)

Potential is potential energy per charge: V = U/q; unit: 1 V = 1 J/C. V is a property of location, not of the test charge.

Potential energy change from potential difference

A charge q moved through potential difference ΔV changes potential energy by ΔU = qΔV.

Electric potential of a point charge

With V = 0 at infinity, the potential due to point charge Q at distance r is V = kQ/r (a scalar; sign matters).

Superposition of electric potential

Net potential is the algebraic (scalar) sum: V_net = V₁ + V₂ + … = k(Q₁/r₁ + Q₂/r₂ + …).

Electric potential is scalar

Electric potential adds without vector components; having a sign does not make it a vector.

Field–potential relationship

Potential difference relates to electric field by ΔV = −∫⃗E · d⃗s (general definition).

Uniform electric field potential change

For uniform ⃗E and straight displacement d: ΔV = −Ed cosθ (parallel: θ=0 ⇒ ΔV=−Ed; perpendicular: θ=90° ⇒ ΔV=0).

Parallel-plate field magnitude

Between large oppositely charged plates (away from edges), the field is approximately uniform with magnitude E = |ΔV|/d.

Acceleration of a charge in a uniform field

A charge in a uniform field has constant acceleration: ⃗a = (q⃗E)/m; negative charges accelerate opposite ⃗E.