AP Physics C E&M Units 1-3

Coulomb’s Law

F = k q1 q2 / r^2

Electric field of a point charge

E = k q / r^2

Electric force in an electric field

F = qE

Direction of electric force

Along E for positive charge, opposite for negative

Superposition principle

Fields and potentials add from all charges

Electric potential of a point charge

V = k q / r

Why electric potential is scalar

It has no direction so it adds algebraically

Electric potential energy

U = k q1 q2 / r

Potential energy change

U = −qΔV

Work done by electric field

W = qΔV

High electric field means

Potential changes rapidly with position

Equipotential surfaces

Electric field is perpendicular

Electric field between plates

ΔV = Ed

When ΔV = Ed applies

Only for uniform electric fields

Electric flux

Φ = EA cosθ

Gauss’s Law

Φ = Qenc / ε0

When to use Gauss’s Law

High symmetry (sphere, cylinder, plane)

Capacitance definition

C = Q / V

Parallel-plate capacitance

C = ε0 A / d

Capacitance with dielectric

C = κε0 A / d

What a dielectric does

Increases capacitance, reduces electric field

Charge on a surface

Q = σA

Electric field from surface charge

E = σ / ε0

Energy stored in capacitor

U = 1/2 C V^2

Energy stored in capacitor (charge form)

U = Q^2 / (2C)

Energy stored is located

In the electric field

Capacitors in series (total)

1/C_total = Σ(1/C)

Capacitors in parallel (total)

C_total = ΣC

Series capacitors have

Same charge, different voltages

Parallel capacitors have

Same voltage, different charges

Charge-voltage relation

Q = CV

Current definition

I = V / R

What current actually is

Flow of charge

Resistance of a wire

R = ρL / A

What resistance depends on

Material, length, cross-sectional area

Resistivity definition

ρ = 1 / σ

Temperature dependence of resistivity

ρ = ρ0(1 + α(T − T0))

Resistors in series (total)

R_total = ΣR

Resistors in parallel (total)

1/R_total = Σ(1/R)

Series resistors have

Same current, different voltages

Parallel resistors have

Same voltage, different currents

Ohm’s Law condition

Material must be ohmic

Electric power

P = IV

Electric power (current form)

P = I^2R

Electric power (voltage form)

P = V^2 / R

Power in a resistor

Rate of thermal energy transfer

EMF definition

ε = ΔW / Δq

Terminal voltage

V = ε − Ir

Kirchhoff’s junction rule

ΣIin = ΣIout

Kirchhoff’s loop rule

ΣΔV = 0

What junction rule represents

Charge conservation

What loop rule represents

Energy conservation

RC time constant

τ = RC

Meaning of time constant

Time to reach about 63 percent of final value

Charging capacitor voltage

VC = ε(1 − e^(−t/RC))

Discharging capacitor voltage

VC = V0 e^(−t/RC)

Charging current behavior

Starts max and decays exponentially

Capacitor at t = 0

Behaves like a wire

Capacitor at long time

Behaves like an open circuit

Specific heat equation

Q = mcΔT

Specific heat relevance

Thermal physics, not E&M

Common AP mistake

Mixing electric field direction with potential change

Best first step in E&M problems

Draw field directions and label charge signs

Time for liquid to evaporate given mass.

t=mL/VI