Electric Charges, Fields, and Gauss's Law

Six topics on the force between charges and the field that carries it. Coulomb's law as a magnitude plus a direction read from the geometry, conservation of charge through friction, contact and induction, the electric field and what its lines do and do not mean, fields of continuous distributions by integration, electric flux through an oriented surface, and Gauss's law, which turns enough symmetry into a field in one line.

AP exam 15-25%6 topics

Topics

8.1

Electric Charge and Electric Force

Conservation of Electric Charge and the Process of Charging

Electric Fields

Electric Fields of Charge Distributions

Electric Flux

Gauss's Law

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Coulomb's law (magnitude)

F = k|q₁||q₂| / r², direction from the picture: unlike attract, like repel

Coulomb constant

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

Electric field

E = F / q₀ (force per unit POSITIVE test charge); F = qE

Point charge

E = kq / r², radially out from +q, in toward −q

Superposition

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

Continuous distribution

dE = k dq / r², integrate WITH direction. r and the projection angle usually vary element to element

Charge densities

dq = λ dx (line), σ dA (surface), ρ dV (volume)

Elementary charge

e = 1.6 × 10⁻¹⁹ C. Free charge is an integer multiple of it

Electric flux

Φ = EA cosθ, with θ measured to the surface NORMAL. Surface parallel to E carries zero flux

Gauss's law

net flux through a CLOSED surface = q(enclosed) / ε₀

What E means there

the TOTAL field, outside sources included. Outside charge contributes zero NET flux, not zero field

When it hands you E

only when symmetry makes E·dA simple: E constant and normal on the flux-carrying part of the surface, zero flux through the rest (a cylinder's end caps, where E runs parallel). Sphere, infinite cylinder, infinite plane

Uniform shell

inside: E = 0. outside: E = kQ / r², as if all the charge sat at the center

Uniform solid sphere (insulating)

inside: E = kQr / R³, rising linearly. outside: E = kQ / r²

Infinite sheet

E = σ / (2ε₀), the SAME at every distance

Just outside a conductor

E = σ / ε₀, twice the lone-sheet value, because the interior field is zero

Infinite line

E = 2kλ / r = λ / (2πε₀r)

Unit 8 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 6 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.