#AP Physics 2: Electricity, Circuits, and Magnetism - Your Ultimate Study Guide

Hey there, future AP Physics 2 master! 👋 Let's dive into the exciting world of electromagnetism. This guide is designed to be your go-to resource, especially the night before the exam. We'll break down complex topics, highlight key concepts, and make sure you're feeling confident and ready to ace that test!

#Introduction to Electromagnetism

In AP Physics 2, we shift our focus from mechanics (like forces and motion) to the fascinating realm of electromagnetism, along with other topics like fluids, thermodynamics, optics, and modern physics. Electromagnetism is HUGE, so we'll tackle it in three main parts: electricity, circuits, and magnetism.

#From Mass to Charge

In mechanics, we dealt with mass, a fundamental property of matter. Now, we're diving into charge, another fundamental property. Get ready to explore the microscopic world—we're going smaller than you're used to!

#Objects vs. Systems

The AP loves to test your understanding of objects and systems. Let's clarify the difference:

• Object: A collection of matter. It could be a single entity or multiple entities grouped together.
• System: A collection of objects being studied as a whole, defined by its boundaries (physical or conceptual).

Think of it this way: objects make up systems. The properties of the objects influence the behavior of the system. Sometimes, the system's internal structure isn't crucial, and we can treat the whole system as a single object.

Example: A balloon filled with gas. The gas and the balloon are objects; together, they form a system. If we're just looking at the overall temperature, we can treat the balloon-gas system as a single object.

#Electric Systems and Objects

Here are some examples of electric systems and objects you'll encounter in this unit:

• Electric Circuits: Closed loops of components allowing electricity to flow (e.g., household circuits, car electrical systems).
• Electric Generators: Convert mechanical energy to electrical energy (e.g., hydroelectric generators, wind turbines).
• Electric Motors: Convert electrical energy to mechanical energy (e.g., car engines, fan motors).
• Batteries: Store electrical energy (e.g., alkaline, lithium-ion).
• Electric Charges: Fundamental property of matter (e.g., electrons, protons, ions).
• Electric Fields: Regions where electric charges experience forces (e.g., around charged objects, between charged plates).
• Electric Potential: Measure of potential energy of a charge in an electric field (e.g., voltage).

#Unit 1: Electricity

#Electric Charge

• Two Types of Charge: Positive (protons) and negative (electrons). Like charges repel, and opposite charges attract.
• Quantization of Charge: Charge is quantized, meaning it comes in discrete units. The smallest unit is the elementary charge, e, which is the magnitude of the charge of a single proton or electron ($e = 1.602 × 10^{-19}$ C).
• Conservation of Charge: The total charge in an isolated system remains constant. Charge cannot be created or destroyed, only transferred. 💡

#Coulomb's Law

Coulomb's Law describes the force between two point charges. The force is:

$$F = k \frac{|q_1q_2|}{r^2}$$

where:

• F is the magnitude of the electric force
• k is Coulomb's constant ($k ≈ 8.99 × 10^9 Nm^2/C^2$)
• $q_1$ and $q_2$ are the magnitudes of the charges
• r is the distance between the charges

#Electric Fields

An electric field is a vector field that describes the electric force experienced by a charge at a given point in space. It's defined as the force per unit charge:

$$E = \frac{F}{q}$$

• Field Lines: Electric field lines point away from positive charges and toward negative charges. The density of lines indicates the strength of the field.
• Uniform Electric Field: The electric field between two parallel charged plates is uniform (constant magnitude and direction).

#Electric Potential and Potential Energy

• Electric Potential (V): The potential energy per unit charge at a point in an electric field. It's measured in volts (V).

$$V = \frac{U}{q}$$

• Electric Potential Energy (U): The energy a charge possesses due to its position in an electric field.

$$U = qV$$

• Potential Difference (ΔV): The difference in electric potential between two points. Also known as voltage. It's what drives current in a circuit.

#Capacitance

• Capacitor: A device that stores electrical energy by accumulating charge on its plates.
• Capacitance (C): The ability of a capacitor to store charge. It's measured in farads (F).

$$C = \frac{Q}{V}$$

• Parallel Plate Capacitor: The capacitance of a parallel plate capacitor is given by:

$$C = \frac{\epsilon_0 A}{d}$$

where:

• $\epsilon_0$ is the permittivity of free space
• A is the area of the plates
• d is the distance between the plates

Capacitance is a high-value topic. Make sure you understand how capacitors work and how to calculate capacitance and stored energy.

#Energy Stored in a Capacitor

The energy stored in a capacitor is given by:

$$U = \frac{1}{2}CV^2 = \frac{1}{2}QV = \frac{Q^2}{2C}$$

Practice Question

**Multiple Choice:**

1. Two point charges, +Q and -Q, are placed a distance r apart. What happens to the magnitude of the electric force if the distance is doubled? (A) It is reduced to 1/4 of its original value. (B) It is reduced to 1/2 of its original value. (C) It doubles. (D) It quadruples.

2. A parallel-plate capacitor has a charge Q and a voltage V. If the distance between the plates is doubled while the charge remains constant, what happens to the voltage? (A) It is reduced to 1/4 of its original value. (B) It is reduced to 1/2 of its original value. (C) It doubles. (D) It quadruples.

Free Response:

A parallel-plate capacitor with capacitance C is charged to a voltage V and then disconnected from the battery. A dielectric material with a dielectric constant k is inserted between the plates of the capacitor.

(a) What happens to the charge on the capacitor? Explain. (b) What happens to the voltage across the capacitor? Explain. (c) What happens to the capacitance of the capacitor? Explain. (d) What happens to the energy stored in the capacitor? Explain.

Scoring Guide

(a) 1 point: The charge remains the same because the capacitor is disconnected from the battery. (b) 2 points: The voltage decreases by a factor of k because the capacitance increases by a factor of k and Q = CV. (c) 1 point: The capacitance increases by a factor of k because the dielectric is inserted. (d) 2 points: The energy decreases by a factor of k because the voltage decreased by a factor of k and U = 1/2 CV^2.

#Unit 2: Circuits

#Electric Current

• Current (I): The rate of flow of electric charge. It's measured in amperes (A).

$$I = \frac{\Delta Q}{\Delta t}$$

• Conventional Current: The direction of current is defined as the direction that positive charges would flow (even though in reality, it's electrons that move).

#Resistance

• Resistance (R): The opposition to the flow of current. It's measured in ohms (Ω).

$$R = \frac{V}{I}$$

• Resistivity (ρ): A material property that determines how much it resists the flow of current.

$$R = \frac{\rho L}{A}$$

where:

• L is the length of the resistor
• A is the cross-sectional area of the resistor

#Ohm's Law

Ohm's Law relates voltage, current, and resistance:

$$V = IR$$

#Series and Parallel Circuits

• Series: Components are connected end-to-end, so the same current flows through each. The total resistance is the sum of individual resistances:

$$R_{total} = R_1 + R_2 + R_3 + ...$$

• Parallel: Components are connected side-by-side, so the voltage across each is the same. The reciprocal of the total resistance is the sum of the reciprocals of individual resistances:

$$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$$

#Power in Circuits

• Electric Power (P): The rate at which electrical energy is converted into other forms of energy. It's measured in watts (W).

$$P = IV = I^2R = \frac{V^2}{R}$$

#Kirchhoff's Rules

Kirchhoff's rules are used to analyze complex circuits:

• Junction Rule: The sum of currents entering a junction equals the sum of currents leaving the junction (conservation of charge).
• Loop Rule: The sum of potential differences around any closed loop in a circuit is zero (conservation of energy).

#RC Circuits

• RC Circuit: A circuit containing a resistor and a capacitor. The capacitor charges or discharges exponentially.
• Time Constant (τ): The time it takes for the capacitor to charge to about 63% of its maximum charge or discharge to about 37% of its initial charge.

$$\tau = RC$$

Practice Question

**Multiple Choice:**

1. A resistor with resistance R is connected to a battery with voltage V. If a second resistor with resistance R is connected in series with the first resistor, what happens to the total current in the circuit? (A) It doubles. (B) It remains the same. (C) It is reduced to 1/2 of its original value. (D) It is reduced to 1/4 of its original value.

2. A 10 Ω resistor and a 20 Ω resistor are connected in parallel. What is the equivalent resistance of the combination? (A) 30 Ω (B) 15 Ω (C) 20/3 Ω (D) 2/30 Ω

Free Response:

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series.

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

Scoring Guide

(a) 1 point: Correct circuit diagram. (b) 1 point: Total resistance = 4 Ω + 6 Ω = 10 Ω. (c) 1 point: Current = V/R = 12 V / 10 Ω = 1.2 A. (d) 1 point: Voltage drop across 4 Ω resistor = IR = 1.2 A * 4 Ω = 4.8 V. (e) 2 points: Power = I^2R = (1.2 A)^2 * 6 Ω = 8.64 W.

#Unit 3: Magnetism

#Magnetic Fields

• Magnetic Field (B): A region of space where a magnetic force can be detected. It's measured in teslas (T).
• Magnetic Field Lines: Magnetic field lines point from the north pole to the south pole outside a magnet. They form closed loops.

#Magnetic Force on a Moving Charge

The magnetic force on a moving charge is given by:

$$F = qvB\sin(\theta)$$

where:

• q is the charge
• v is the velocity of the charge
• B is the magnetic field
• $\theta$ is the angle between the velocity and the magnetic field

#Magnetic Force on a Current-Carrying Wire

The magnetic force on a current-carrying wire is given by:

$$F = ILB\sin(\theta)$$

where:

• I is the current
• L is the length of the wire
• B is the magnetic field
• $\theta$ is the angle between the current and the magnetic field

#Sources of Magnetic Fields

• Current-Carrying Wire: A current-carrying wire produces a magnetic field around it. The field lines form concentric circles around the wire.
• Solenoid: A coil of wire that produces a magnetic field similar to that of a bar magnet when current flows through it.
• Electromagnet: A magnet created by an electric current. The strength of the magnetic field can be controlled by the amount of current.

#Faraday's Law of Induction

Faraday's Law describes how a changing magnetic field can induce an electromotive force (EMF) or voltage in a loop of wire:

$$EMF = -N\frac{\Delta\Phi}{\Delta t}$$

where:

• N is the number of turns in the coil

• $\frac{\Delta\Phi}{\Delta t}$ is the rate of change of magnetic flux

• Magnetic Flux (Φ): A measure of the total magnetic field passing through a given area.

$$\Phi = BA\cos(\theta)$$

where:

• B is the magnetic field
• A is the area
• $\theta$ is the angle between the magnetic field and the normal to the area

Faraday's Law is a key concept. Make sure you understand how a changing magnetic field induces an EMF.

#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 produces it. In other words, the induced current creates a magnetic field that counteracts the original change.

#Transformers

• Transformer: A device that uses electromagnetic induction to change the voltage of an alternating current.
• Step-Up Transformer: Increases the voltage.
• Step-Down Transformer: Decreases the voltage.

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

where:

• $V_p$ is the voltage in the primary coil
• $V_s$ is the voltage in the secondary coil
• $N_p$ is the number of turns in the primary coil
• $N_s$ is the number of turns in the secondary coil

Practice Question

**Multiple Choice:**

1. A charged particle moves through a uniform magnetic field. Under what condition will the magnetic force on the particle be zero? (A) When the particle is stationary. (B) When the particle's velocity is parallel to the magnetic field. (C) When the particle's velocity is perpendicular to the magnetic field. (D) When the particle's charge is zero.

2. A loop of wire is placed in a uniform magnetic field. If the area of the loop is increased, what happens to the magnetic flux through the loop? (A) It decreases. (B) It remains the same. (C) It increases. (D) It becomes zero.

Free Response:

A rectangular loop of wire with dimensions 0.2 m by 0.3 m is placed in a uniform magnetic field of 0.5 T. The loop is initially oriented such that its normal is parallel to the magnetic field. The loop is then rotated 90 degrees in 0.1 s so that its normal is perpendicular to the magnetic field.

(a) Calculate the initial magnetic flux through the loop. (b) Calculate the final magnetic flux through the loop. (c) Calculate the average EMF induced in the loop during the rotation. (d) If the loop has a resistance of 2 Ω, calculate the average current induced in the loop.

Scoring Guide

(a) 1 point: Initial flux = BAcos(0) = 0.5 T * (0.2 m * 0.3 m) * 1 = 0.03 Wb. (b) 1 point: Final flux = BAcos(90) = 0.5 T * (0.2 m * 0.3 m) * 0 = 0 Wb. (c) 2 points: Average EMF = -ΔΦ/Δt = -(0 - 0.03 Wb) / 0.1 s = 0.3 V. (d) 2 points: Average current = EMF/R = 0.3 V / 2 Ω = 0.15 A.

#Final Exam Focus

#High-Priority Topics

• Electricity: Coulomb's Law, electric fields, electric potential, capacitance, energy stored in capacitors.
• Circuits: Ohm's Law, series and parallel circuits, Kirchhoff's rules, power in circuits, RC circuits.
• Magnetism: Magnetic forces on moving charges and current-carrying wires, Faraday's Law, Lenz's Law, transformers.

#Common Question Types

• Multiple Choice: Conceptual questions on electric fields, circuits, and magnetic forces. Calculations involving Coulomb's Law, Ohm's Law, and capacitance.
• Free Response: Circuit analysis, calculations involving induced EMF, and qualitative explanations of electromagnetic phenomena.

#Last-Minute Tips

• Time Management: Quickly identify the type of problem and apply the appropriate formulas. Don't get bogged down on a single question.
• Common Pitfalls: Be careful with units and signs. Double-check your calculations. Remember the difference between series and parallel circuits.
• Strategies: Draw diagrams to visualize problems. Write down all knowns and unknowns. Use your formula sheet effectively.

#Final Thoughts

You've got this! You've reviewed the key concepts, practiced the problem-solving techniques, and now you're ready to show the AP Physics 2 exam what you're made of. Stay calm, stay focused, and trust in your preparation. Good luck! 💪