Electric Force, Field, and Potential

Seven topics on the force between charges and the two maps that describe it. Coulomb's law as a magnitude plus a direction read from the arrangement, conservation of charge through friction, contact and induction, the electric field and what its lines do and do not mean, potential energy summed pair by pair with its signs kept, potential as a scalar attached to a place, capacitors and the difference between a connected battery and a disconnected one, and energy conservation where kinematics stops working.

AP exam 15-18%7 topics

Topics

10.1

Electric Charge and Electric Force

Conservation of Electric Charge and the Process of Charging

Electric Fields

Electric Potential Energy

Electric Potential

Capacitors

Conservation of Electric Energy

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Coulomb's law (magnitude)

F = k|q₁||q₂| / r². Direction from the arrangement: unlike attract, like repel, along the line joining them

Coulomb constant

k = 1 / (4πε₀) = 8.99 × 10⁹ N·m²/C². Use k OR ε₀, never both in one expression

Newton's third law

both charges feel the SAME magnitude, however lopsided. What differs is a = F/m

Elementary charge

e = 1.6 × 10⁻¹⁹ C. Free charge is an integer multiple of it, and charge is conserved in every transfer

Electric field

E = F / q, in N/C or V/m. Set by the SOURCES; the test charge divides out

Force on a charge

F = qE, keeping the sign of q. A negative charge is pushed OPPOSITE the field

Point charge

E = k|q| / r², out from a positive source, in toward a negative one

Superposition

add contributions as VECTORS, components first. A charge never contributes to the field acting on itself

Field lines

direction of the force, not a trajectory. Density carries strength; blank space is not zero field; lines never cross

Conductor at equilibrium

excess charge on the SURFACE, E = 0 inside the metal, E perpendicular just outside. An insulator keeps charge where it was put

Between parallel plates

E = V/d, UNIFORM across the gap. Constant force means projectile-style motion

Potential energy of a pair

U = kq₁q₂ / r, SIGNED. Negative means bound; separating a bound pair raises U toward zero

Several charges

one term per distinct PAIR: 3 charges give 3 pairs, 4 charges give 6

Potential

V = kq / r, a SCALAR belonging to a location. Volts = joules per coulomb

Adding potentials

signed numbers, term by term. No components, no angles: geometry enters only through r

Energy of a charge

U = qV. Potential describes the place; potential energy belongs to the charge you put there

Field from potential

E = V/d is the AVERAGE over the interval, exact only where the field is uniform. Measure d ALONG the field

Equipotentials

no work to move along one; field lines cross them at right angles and point toward LOWER potential

Capacitance

C = Q/V, fixed by hardware: C = κε₀A/d. Charging harder does not change it

Which quantity is pinned

battery attached: V fixed, Q = CV moves. Battery disconnected: Q fixed, V = Q/C moves

Stored energy

U = ½CV² = Q²/(2C) = ½QV. QUADRATIC: twice the voltage stores four times the energy

Energy conservation

ΔK = −ΔU = q(V(start) − V(end)), signs kept. Use this whenever the field changes along the path

Unit 10 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 7 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

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Check what stuck.

Units 9 through 10, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 42questions

13topics

48codes covered

Begin assessment →