AP Physics C: Electricity and Magnetism Study Guide

1. Introduction to AP Physics C: Electricity and Magnetism

AP Physics C: Electricity and Magnetism focuses on the study of electric fields, magnetic fields, and circuits, with an emphasis on problem-solving and conceptual understanding. The course covers topics using calculus to describe physical systems.

Exam Format:

• Multiple-Choice Questions: Assess knowledge of the topics and problem-solving abilities.
• Free-Response Questions: Require the application of concepts to real-world scenarios.

2. Electrostatics

Coulomb's Law:

• The force between two point charges is given by:
  • F = kₑ * |q₁ * q₂| / r²
  • Where:
    • kₑ = 8.99 × 10⁹ N·m²/C² is Coulomb's constant,
    • q₁ and q₂ are the charges,
    • r is the distance between the charges.

Electric Field (E):

• The electric field due to a point charge is given by:
  • E = kₑ * q / r²
• The direction of the electric field is radially outward from a positive charge and inward toward a negative charge.

Electric Potential Energy (U):

• The potential energy between two point charges is given by:
  • U = kₑ * q₁ * q₂ / r
• The electric potential energy represents the work required to bring the charges from infinity to a distance r.

Electric Potential (V):

• The electric potential at a point due to a point charge is:
  • V = kₑ * q / r
• The electric potential is the amount of electric potential energy per unit charge.

Gauss's Law:

• Gauss’s law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface:
  • ∮E · dA = Q_enclosed / ε₀
  • Where:
    • E is the electric field,
    • dA is the differential area element,
    • Q_enclosed is the enclosed charge,
    • ε₀ = 8.85 × 10⁻¹² C²/N·m² is the permittivity of free space.

3. Conductors, Capacitors, and Dielectrics

Capacitance (C):

• The capacitance of a parallel-plate capacitor is given by:
  • C = ε₀ * A / d
  • Where:
    • A is the area of one of the plates,
    • d is the distance between the plates,
    • ε₀ is the permittivity of free space.

Energy Stored in a Capacitor:

• The energy stored in a capacitor is given by:
  • U = ½ * C * V²
  • Where:
    • C is the capacitance,
    • V is the voltage across the capacitor.

Dielectrics:

• A dielectric material is inserted between the plates of a capacitor, increasing the capacitance by a factor of the dielectric constant (κ):
  • C' = κ * C

4. Current, Resistance, and DC Circuits

Current (I):

• Current is the rate of flow of charge:
  • I = ΔQ / Δt
  • Where ΔQ is the charge flowing through a cross-sectional area in a time Δt.

Ohm's Law:

• Ohm’s law relates current, voltage, and resistance:
  • V = I * R
  • Where:
    • V is the voltage,
    • I is the current,
    • R is the resistance.

Resistivity (ρ):

• The resistance of a wire depends on the material’s resistivity, length, and cross-sectional area:
  • R = ρ * (L / A)
  • Where:
    • ρ is the resistivity,
    • L is the length of the conductor,
    • A is the cross-sectional area.

Power (P):

• The electrical power dissipated in a resistor is given by:
  • P = I * V = I² * R = V² / R

5. Magnetic Fields

Magnetic Force on a Moving Charge:

• The magnetic force on a moving charge is given by:
  • F = q * v * B * sin(θ)
  • Where:
    • q is the charge,
    • v is the velocity of the charge,
    • B is the magnetic field strength,
    • θ is the angle between the velocity and the magnetic field.

Magnetic Field due to a Current:

• The magnetic field around a long, straight current-carrying wire is given by:
  • B = (μ₀ * I) / (2π * r)
  • Where:
    • μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space,
    • I is the current,
    • r is the radial distance from the wire.

Ampère’s Law:

• Ampère’s law relates the magnetic field around a current-carrying conductor to the current enclosed by a loop:
  • ∮B · dl = μ₀ * I_enclosed

6. Electromagnetic Induction

Faraday’s Law of Induction:

• Faraday’s law states that the induced EMF in a loop is proportional to the rate of change of magnetic flux through the loop:
  • ε = -dΦ/dt
  • Where:
    • Φ is the magnetic flux.

Lenz’s Law:

• Lenz’s law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it.

Inductance (L):

• The inductance of a coil is the ratio of the induced EMF to the rate of change of current:
  • L = N * Φ / I
  • Where:
    • N is the number of turns in the coil,
    • Φ is the magnetic flux.

Energy Stored in an Inductor:

• The energy stored in an inductor is given by:
  • U = ½ * L * I²
  • Where:
    • L is the inductance,
    • I is the current.

7. AC Circuits

Impedance (Z):

• The impedance of a circuit with resistance (R) and reactance (X) is given by:
  • Z = √(R² + X²)

Resonance in LC Circuits:

• Resonance occurs when the inductive reactance and capacitive reactance are equal, causing the impedance to be at a minimum and current to be at a maximum:
  • f₀ = 1 / (2π√(LC))
  • Where:
    • f₀ is the resonant frequency,
    • L is the inductance,
    • C is the capacitance.

8. Maxwell’s Equations

Gauss’s Law for Electricity:

• ∮E · dA = Q_enclosed / ε₀

Gauss’s Law for Magnetism:

• ∮B · dA = 0
  • This law states that there are no magnetic monopoles.

Faraday’s Law of Induction:

• ∮E · dl = -dΦ/dt

Ampère’s Law with Maxwell’s Addition:

• ∮B · dl = μ₀ * (I_enclosed + ε₀ * dΦ/dt)