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AP Physics 2: Algebra-Based · Unit 2 of 7

Electric Force, Field, and Potential

15–18% of the exam8 lessons · 109 min47 terms
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What this unit covers

The topics below follow the published Physics 2 course framework for Unit 2. This unit is worth 15–18% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Coulomb’s lawElectric fieldsElectric potentialCharge distributions

Lessons in this unit

Formulas in Unit 2

Coulomb’s law
F = k · |q₁ · q₂| / r²
k = 8.99 × 10⁹ N·m²·C⁻² (often rounded to 9.0 × 10⁹). r is the center-to-center distance. The force acts along the line joining the charges: repulsive for like charges, attractive for opposite.
Electric field: definition and point-charge value
E = F / q and E = k · |Q| / r²
Units are N·C⁻¹ (equivalently V·m⁻¹). The first form gives the force felt by a charge q in a field; the second gives the field a source charge Q creates at distance r.
Potential of a point charge & energy of a charge
V = k · Q / r and ΔU = q · ΔV
Keep the sign of Q in V = kQ/r: a positive charge makes V positive, a negative charge makes V negative. ΔU is the energy change when a charge q moves through a potential difference ΔV.
Uniform field and potential
E = V / d
Between two parallel plates a distance d apart with a voltage V across them, the field is uniform with magnitude V/d. This is why field units can be written as V·m⁻¹.
Uniform field between parallel plates
E = V / d
Two large parallel plates with a voltage V across a gap d produce a nearly uniform field V/d, pointing from the positive plate to the negative plate. This is the geometry of a parallel-plate capacitor.
Superposition
E_net,x = Σ E_i cos θ_i and E_net,y = Σ E_i sin θ_i, then |E| = √(E_x² + E_y²) · V_net = Σ kq_i/r_i (signed, no components)
Use the magnitude kq/r² for each field contribution and let the geometry set the direction. Keep the sign of q for potential.
Field from potential
for a uniform field: E = ΔV/d, in volts per meter · the field points from HIGH potential toward LOW
V/m and N/C are the same unit. Field points downhill on the potential landscape, which is why a positive charge released at rest moves toward lower potential.
The two routes
kinematic: a = qE/m, then use the constant-acceleration equations · energy: qΔV = ½mv² − ½mv₀², so v = √(2qΔV/m) from rest
Use energy when the question gives a potential difference and asks for speed. Use kinematics when it gives geometry and asks for deflection or time.
Three symmetric geometries
sphere or shell, outside: E = kQ/r² (behaves like a point charge at the center) · inside a shell: E = 0 · large charged plate: E is uniform, independent of distance · long wire: E ∝ 1/r
These follow from symmetry. An algebra-based course states them rather than deriving them from Gauss's law, but the reasoning is the same.

Every term in Unit 2

All 47 terms we publish for Electric Force, Field, and Potential, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Uniform field between parallel plates
E = V/d, directed from the positive plate to the negative plate. The equipotential surfaces are planes parallel to the plates.
Charge conservation and quantization
Charge is never created or destroyed, only transferred, and comes in multiples of the elementary charge 1.6 × 10⁻¹⁹ C.
Coulomb's law
F = kq₁q₂/r² with k = 8.99 × 10⁹ N·m²/C². Like charges repel, opposite attract, and force falls with the square of separation.
Charging by friction, conduction and induction
Friction transfers electrons between materials; conduction requires contact and shares charge; induction polarizes then grounds, leaving opposite charge without contact.
Polarization of a neutral object
Charge redistribution within a neutral object near a charged one. Explains why a charged rod attracts neutral paper.
Electric field
E = F/q, force per unit positive test charge, in N/C. Points away from positive charge and toward negative.
Field of a point charge
E = kq/r². Field lines never cross, start on positive charge and end on negative, and their density represents field strength.
Electric potential energy
U = kq₁q₂/r for two point charges, and includes sign. Like charges have positive potential energy that decreases as they separate.
Electric potential
V = U/q, energy per unit charge, in volts. A scalar, so potentials from several charges add algebraically without vectors.
Potential difference and work
W = qΔV. Moving a charge along an equipotential surface requires no work, since ΔV is zero.
Equipotential lines
Always perpendicular to field lines. Closely spaced equipotentials indicate a strong field.
Field vs potential
Field is a vector and can be zero where potential is not; potential is a scalar and can be zero where field is not. Between two equal opposite charges, the midpoint has V = 0 but E ≠ 0.
Conductors vs insulators
Conductors have mobile charge carriers that redistribute freely; insulators hold charge where it is placed, which is why only conductors can be charged by induction.
Grounding
Connecting to a large reservoir of charge, allowing electrons to flow in or out until the object is neutral or at the ground's potential.
Electroscope behavior
Leaves diverge because like charges repel. They diverge for either sign of charge, so an electroscope alone cannot tell you which.
Field line rules
Start on positive and end on negative charge, never cross, and are denser where the field is stronger. They are perpendicular to a conductor surface.
Superposition of fields
Add contributions as vectors, resolving into components first. The point where two fields cancel lies nearer the smaller charge.
Field inside a conductor
Zero at equilibrium, because any field would move charges until it was canceled. All excess charge sits on the surface.
Why potential is a scalar
It is energy per charge, and energy has no direction. This is why V from several charges is a simple sum with signs.
Sketching equipotentials
Draw them perpendicular to field lines and at equal potential intervals; closer spacing indicates a stronger field.
Charged particle released in a uniform field
Experiences constant force and therefore constant acceleration, so the kinematics are identical to projectile motion.
Fields add as vectors, potentials as scalars
Field needs components and recombination; potential is a signed sum with no direction. A point can have zero potential and large field, or the reverse.
The classic midpoint result
Midway between equal and opposite charges the potentials cancel to zero while the two field vectors reinforce. The standard demonstration that V = 0 does not mean E = 0.
Where the net field is zero
Between two LIKE charges, closer to the smaller. OUTSIDE two unlike charges, beyond the smaller. Never between unlike charges.
Keep signs out of field magnitudes
Use kq/r² with |q| and let the geometry set the direction — away from positive, toward negative. Signs belong in potential, not in field magnitude.
Reading field lines
They point the way a positive test charge is pushed, leave positive and enter negative, never cross, and their density represents strength.
Why equipotentials are perpendicular to field lines
Moving along an equipotential does no work, and zero work requires displacement perpendicular to the field. Forced, not conventional.
Field from potential
E = ΔV/d for a uniform field, in V/m — the same unit as N/C. Field points from HIGH potential toward LOW.
Where the topographic analogy breaks
A positive charge moves toward lower potential like a ball downhill; a NEGATIVE charge moves toward higher potential. The landscape inverts with the sign.
Acceleration of a charge in a field
a = qE/m. Not qE — forgetting the mass gives newtons where m/s² is wanted.
Charge in a uniform field is a projectile problem
Constant velocity across the field, constant acceleration along it, time shared. The path is a parabola, for the same reason a thrown ball traces one.
Energy versus kinematics
A potential difference and a speed question means use qΔV = ΔKE. Plate geometry and a deflection question means use kinematics.
Same voltage, same energy, different speeds
A proton and an electron through the same ΔV gain equal kinetic energy. The electron is ~1836× lighter, so it ends far faster.
When gravity matters
Negligible for electrons and protons in laboratory fields. NOT negligible for charged oil drops or dust — a mass in kilograms is the signal that it counts.
Four properties of a conductor in equilibrium
Zero field inside the material, all excess charge on the outer surface, field perpendicular at the surface, and the whole conductor one equipotential.
Faraday cage
A hollow conductor shields its interior from EXTERNAL fields. It does not shield the outside from a charge placed inside the cavity.
Sphere behaves as a point charge
Outside a spherically symmetric distribution, E = kQ/r² exactly as for a point charge at the center. Inside a shell, E = 0.
Zero field with nonzero potential
Inside a charged conductor the field is zero but the potential is a constant nonzero value — set by the work to bring charge from infinity, not by the local field.
Charge concentrates at sharp points
Surface density and therefore local field are greatest where curvature is highest. The operating principle of a lightning rod.
Coulomb versus Newton
Both go as 1/r², but the electric force can attract OR repel and is roughly 10³⁶ times stronger between two protons than their gravitational attraction.
Charge is conserved and quantized
It comes in multiples of e = 1.60 × 10⁻¹⁹ C and the total in a closed system never changes. Charging by friction moves charge; it does not create it.
Conduction versus induction versus polarization
Conduction transfers charge by contact. Induction separates charge using a nearby charge, then grounds one side. Polarization only shifts charge within molecules — the object stays neutral.
Why a charged rod attracts neutral paper
Polarization. The near side of each molecule is attracted slightly more than the far side is repelled, because the field is stronger closer to the rod.
Potential difference does the work
W = qΔV, so only the DIFFERENCE matters physically. Choosing where V = 0 is a convention, usually infinity for point charges or the negative plate for capacitors.
Electron-volt as an energy
The energy an electron gains crossing one volt: 1.60 × 10⁻¹⁹ J. Not a voltage, despite the name.
Capacitance of parallel plates
C = Q/V, and for parallel plates C = ε₀A/d. Adding a dielectric raises C, which is why real capacitors are not air-filled.
Why the energy of a capacitor carries a factor of one half
U = ½CV² = ½QV = Q²/2C. The factor of ½ appears because the voltage grows as the charge accumulates.

What examiners penalize here

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

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Questions about this unit

How much of the AP Physics 2: Algebra-Based exam is Unit 2?

Unit 2, Electric Force, Field, and Potential, is worth 15–18% of the Physics 2 multiple-choice section according to the published course framework. Across all 7 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Physics 2 Unit 2?

Electric Force, Field, and Potential covers Coulomb’s law, Electric fields, Electric potential and Charge distributions. We publish 47 terms with definitions for this unit, all of them on this page.

How should I study Physics 2 Unit 2?

Read the 8 lessons below first — about 110 minutes — then drill the 47 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 7 units of AP Physics 2: Algebra-Based

  1. Unit 1 · Thermodynamics
  2. Unit 2 · Electric Force, Field, and Potential
  3. Unit 3 · Electric Circuits
  4. Unit 4 · Magnetism and Electromagnetism
  5. Unit 5 · Geometric Optics
  6. Unit 6 · Waves, Sound, and Physical Optics
  7. Unit 7 · Modern Physics

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 2: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.