#AP Physics 2: Ultimate Study Guide 🚀

Hey there, future physicist! Let's get you prepped and confident for the AP Physics 2 exam. This guide is designed to be your go-to resource, especially the night before the test. We'll break down the key concepts, highlight important connections, and give you the tools you need to succeed. Let's do this!

#1. Electrostatics

#1.1 Conservation of Electric Charge

• Fundamental Principle: The net charge of an isolated system is always conserved.

• Charge Transfer: When objects touch, charge is redistributed until they reach equilibrium.

• Net Charge: The total charge before and after any interaction remains the same.

  

  Caption: When two charged spheres touch, charge is transferred until they reach the same charge.

#CollegeBoard Essential Knowledge:

• Charging by Conduction: Direct contact leads to charge sharing, conserving total system charge.
• Induction: A charged object can cause charge separation in a neutral object nearby.
• Grounding: Excess charge is transferred to/from a large reservoir (like the Earth) 🌎.

#1.2 Conductors and Insulators

• Conductors: Materials with free electrons (e.g., metals like copper, silver, gold). These allow charge to flow easily.

• Insulators: Materials with tightly bound electrons (e.g., rubber, plastic, glass). These resist charge flow.

  

  Caption: Insulators (like rubber) prevent charge from moving, while conductors (like copper) allow charge to flow.

• Electrical Resistance: Conductors have low resistance; insulators have high resistance.

• Electron Mobility: Electrons move easily in conductors, not so much in insulators.

#Example Questions:

Example 1: A copper wire has a length of 1 meter and a cross-sectional area of 0.1 square millimeters. The wire has a resistance of 1 ohm. What is the resistivity of the wire?

Solution:

Using the formula $\rho = \frac{RA}{L}$, we get $\rho = \frac{(1 \Omega)(0.1 \times 10^{-6} m^2)}{1 m} = 1 \times 10^{-7} \Omega \cdot m$. Note that you need to convert $mm^2$ to $m^2$.

Example 2: A copper wire has a length of 2 meters and a cross-sectional area of 0.2 square millimeters. The wire has a resistivity of $1 \times 10^{-7} \Omega \cdot m$. What is the resistance of the wire?

Solution:

Using the formula $R = \frac{\rho L}{A}$, we get $R = \frac{(1 \times 10^{-7} \Omega \cdot m)(2 m)}{0.2 \times 10^{-6} m^2} = 1 \Omega$.

Example 3: What is a device called that transfers electric charge? What are its main characteristics?

Solution:

It's called an electric conductor. Main characteristics include low resistance, high electron mobility, and good conductivity.

#2. Electric Fields and Forces

#2.1 Coulomb's Law

• Force Equation: $F = k \frac{|q_1 q_2|}{r^2}$, where:

  • $F$ is the electrostatic force
  • $k$ is Coulomb's constant ($8.99 \times 10^9 N m^2/C^2$)
  • $q_1$ and $q_2$ are the magnitudes of the charges
  • $r$ is the distance between the charges

• Attractive vs. Repulsive:

  • Opposite charges attract (negative force).
  • Like charges repel (positive force).

#2.2 Electric Fields

• Field Definition: Electric field ($E$) is the force per unit charge: $E = \frac{F}{q}$.
• Field from a Point Charge: $E = k \frac{|q|}{r^2}$.
• Field Lines:
  • Point away from positive charges and toward negative charges.
  • The density of lines indicates the field strength.

#2.3 Electric Potential

• Potential Definition: $V = \frac{U}{q}$, where $U$ is the electric potential energy.
• Potential from a Point Charge: $V = k \frac{q}{r}$.
• Potential Difference: $\Delta V = V_B - V_A$, the work done per unit charge to move a charge between two points.

#2.4 Relationship between Electric Field and Potential

• Relationship: $E = -\frac{\Delta V}{\Delta x}$ (in one dimension).
• Equipotential Surfaces: Surfaces where the potential is constant. Electric field lines are always perpendicular to these surfaces.

#3. DC Circuits

#3.1 Current, Resistance, and Ohm's Law

• Current (I): Rate of charge flow: $I = \frac{\Delta Q}{\Delta t}$ (measured in Amperes).
• Resistance (R): Opposition to current flow: $R = \frac{\rho L}{A}$ (measured in Ohms).
• Ohm's Law: $V = IR$ (Voltage = Current x Resistance).

#3.2 Series and Parallel Circuits

• Series Circuits:
  • Current is the same through all components.
  • Total resistance: $R_{total} = R_1 + R_2 + R_3 + ...$
  • Voltage drops add up to the source voltage.
• Parallel Circuits:
  • Voltage is the same across all components.
  • Total resistance: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$
  • Current splits between branches.

#3.3 Power and Energy in Circuits

• Power (P): $P = IV = I^2R = \frac{V^2}{R}$ (measured in Watts).
• Energy (E): $E = Pt$ (measured in Joules).

#4. Magnetism

#4.1 Magnetic Fields

• Magnetic Field (B): Measured in Teslas (T).
• Field Lines:
  • Point from the north pole to the south pole outside the magnet.
  • Form closed loops.
• Force on a Moving Charge: $F = qvB \sin(\theta)$, where:
  • $q$ is the charge
  • $v$ is the velocity of the charge
  • $B$ is the magnetic field strength
  • $\theta$ is the angle between $v$ and $B$

#4.2 Magnetic Force on a Current-Carrying Wire

• Force Equation: $F = ILB \sin(\theta)$, where:
  • $I$ is the current
  • $L$ is the length of the wire
  • $B$ is the magnetic field strength
  • $\theta$ is the angle between $I$ and $B$

#4.3 Sources of Magnetic Fields

• Current in a Wire: A current-carrying wire produces a circular magnetic field around it.
• Solenoids: A coil of wire creates a strong, uniform magnetic field inside it.
• Magnets: Permanent magnets have intrinsic magnetic fields.

#5. Electromagnetism

#5.1 Electromagnetic Induction

• Faraday's Law: The induced EMF (electromotive force) is proportional to the rate of change of magnetic flux: $\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$, where:
  • $\varepsilon$ is the induced EMF
  • $N$ is the number of turns in the coil
  • $\Phi$ is the magnetic flux
• Lenz's Law: The induced current flows in a direction that opposes the change in magnetic flux that produced it. (Nature resists change!)

#5.2 Transformers

• Transformer Equation: $\frac{V_p}{V_s} = \frac{N_p}{N_s}$, where:
  • $V_p$ is the primary voltage
  • $V_s$ is the secondary voltage
  • $N_p$ is the number of turns in the primary coil
  • $N_s$ is the number of turns in the secondary coil
• Power Conservation: $P_p = P_s$ (ideal transformer), so $I_p V_p = I_s V_s$.

#6. Waves and Optics

#6.1 Wave Properties

• Wavelength ($\lambda$): The distance between two consecutive crests or troughs.
• Frequency (f): The number of oscillations per second.
• Amplitude (A): The maximum displacement from equilibrium.
• Wave Speed (v): $v = f \lambda$.

#6.2 Reflection and Refraction

• Reflection: Angle of incidence equals the angle of reflection.
• Refraction: Snell's Law: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where:
  • $n$ is the refractive index of the medium
  • $\theta$ is the angle with respect to the normal

#6.3 Interference and Diffraction

• Interference: Constructive (waves add) and destructive (waves cancel) interference.
• Diffraction: Bending of waves around obstacles or through openings.

#7. Modern Physics

#7.1 Quantum Physics

• Photons: Packets of light energy: $E = hf$, where:
  • $h$ is Planck's constant ($6.626 \times 10^{-34} J \cdot s$)
  • $f$ is the frequency of light
• Wave-Particle Duality: Particles can behave like waves, and waves can behave like particles.
• Energy Levels: Electrons in atoms can only occupy specific energy levels.

#7.2 Nuclear Physics

• Nuclear Reactions: Processes that involve changes in the nucleus.
• Mass-Energy Equivalence: $E = mc^2$ (Mass can be converted into energy and vice versa).
• Radioactivity: Spontaneous emission of particles or energy from unstable nuclei.

#Final Exam Focus

#High-Priority Topics

• Electrostatics: Coulomb's Law, electric fields, and potential.
• Circuits: Ohm's Law, series/parallel circuits, power.
• Magnetism: Magnetic forces, induction, and transformers.
• Waves and Optics: Reflection, refraction, interference, and diffraction.
• Modern Physics: Quantum concepts, photons, and nuclear physics.

#Common Question Types

• Multiple Choice: Conceptual questions, calculations, and graph analysis.
• Free Response: Multi-part problems involving derivations, explanations, and circuit analysis.

#Last-Minute Tips

#Practice Questions

Practice Question

Multiple Choice Questions:

1. Two point charges, +Q and -Q, are separated by a distance d. What happens to the magnitude of the force between them if the distance is doubled? (A) It is reduced by a factor of 4 (B) It is reduced by a factor of 2 (C) It is doubled (D) It is quadrupled

2. A wire carries a current of 2 A. If the wire is placed in a magnetic field of 0.5 T, and the length of the wire within the field is 1 m, what is the magnitude of the force on the wire if the wire is perpendicular to the field? (A) 0.5 N (B) 1 N (C) 2 N (D) 4 N

3. A transformer has 100 turns in its primary coil and 200 turns in its secondary coil. If the primary voltage is 120 V, what is the secondary voltage? (A) 60 V (B) 120 V (C) 240 V (D) 480 V

Free Response Question:

Consider a circuit with a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series.

(a) Draw the circuit diagram. (2 points) (b) Calculate the total resistance of the circuit. (2 points) (c) Calculate the current flowing through the circuit. (2 points) (d) Calculate the voltage drop across the 4 Ω resistor. (2 points) (e) Calculate the power dissipated by the 6 Ω resistor. (2 points)

FRQ Scoring Breakdown:

(a) Correct circuit diagram with battery, 4 Ω resistor, and 6 Ω resistor in series. (2 points) (b) $R_{total} = 4 \Omega + 6 \Omega = 10 \Omega$ (2 points) (c) $I = \frac{V}{R} = \frac{12 V}{10 \Omega} = 1.2 A$ (2 points) (d) $V_{4 \Omega} = IR = 1.2 A \times 4 \Omega = 4.8 V$ (2 points) (e) $P_{6 \Omega} = I^2 R = (1.2 A)^2 \times 6 \Omega = 8.64 W$ (2 points)