#AP Physics 2: Electric Energy & Potential - The Night Before

Hey there, future physicist! Let's get you prepped for the AP Physics 2 exam with a high-impact review of electric energy and potential. This guide is designed to be your best friend tonight, focusing on clarity, quick recall, and those crucial exam connections.

#Conservation of Electric Energy

• Fundamental Principle: A direct consequence of the law of conservation of energy.
• In Circuits: Energy supplied = Energy used + Energy stored. Think of it like a bank account; what goes in must come out (or stay in).
• Applications: Understanding circuits, batteries, generators, and transformers. It's the backbone of electrical analysis!

#Electric Fields & Work

• Definition: Work is done by the field when moving a charge from one point to another.
• Formula: $W = q\Delta V$, where:
  • $W$ = Work (Joules)
  • $q$ = Charge (Coulombs)
  • $\Delta V$ = Change in electric potential (Volts)
• Sign Convention:
  • Positive work: Final potential > Initial potential.
  • Negative work: Final potential < Initial potential.
• Importance: Analyzing circuits and devices, calculating energy stored in capacitors.

#Work and Coulomb's Law

• Bringing like charges together or separating opposite charges requires work.
• Recall: $W = Fd$ (Work = Force x Distance)

-   <math-inline>\Delta U\_E</math-inline> is the change in electric potential energy (a scalar quantity).
-   For multiple charges, sum all individual <math-inline>U\_E</math-inline> values.

#Electric Potential Energy and Electric Field Strength

• Electric potential energy can also be expressed in terms of the electric field strength.

#Electric Potential Energy

• Symbol: $U$ (measured in Joules, J).
• Nature: Scalar (magnitude only, no direction).
• Relationship to Electric Potential: $U = qV$, where $V$ is the electric potential (Volts). Electric potential is potential energy per unit charge.
• Applications: Understanding electric forces and energy in systems with charged particles.
• Energy Conversion: Electric potential energy can convert to kinetic energy (and vice-versa) when charges move in electric fields. Total energy in a closed system is conserved.

#Final Exam Focus

Okay, let's get down to brass tacks. Here's what to focus on for the exam:

• Conservation of Energy: Understand how energy is conserved in circuits and electric fields. This is a recurring theme.
• Work-Energy Theorem: Relate work done by electric fields to changes in potential energy. Remember $W = q\Delta V$.
• Electric Potential vs. Potential Energy: Know the difference and how they relate ($U=qV$).
• Calculations: Practice problems involving work, potential energy, and potential differences.
• Conceptual Understanding: Be able to explain these concepts in your own words, not just recite formulas.

#Last Minute Tips

• Time Management: Don't spend too long on one question. If you're stuck, move on and come back later.
• Units: Always include units in your answers. It's an easy way to pick up points.
• Draw Diagrams: Visualizing the problem can help you understand it better.
• Show Your Work: Even if you get the wrong answer, you can get partial credit for showing your process.
• Stay Calm: You've got this! Take deep breaths and trust your preparation.

#Practice Questions

Practice Question

Multiple Choice Questions

1. A positive charge is moved from point A to point B in an electric field. The work done by the electric field is negative. Which of the following must be true? (A) The electric potential at point A is higher than at point B. (B) The electric potential at point B is higher than at point A. (C) The electric potential at points A and B are the same. (D) The electric field is zero between points A and B.

2. Two parallel plates are charged to create a uniform electric field between them. A proton is released from rest near the positive plate. What will happen to the proton's electric potential energy and kinetic energy as it moves towards the negative plate? (A) Electric potential energy increases, kinetic energy decreases. (B) Electric potential energy decreases, kinetic energy increases. (C) Both electric potential energy and kinetic energy increase. (D) Both electric potential energy and kinetic energy decrease.

3. A capacitor is charged and then disconnected from the battery. If the distance between the plates is doubled, what happens to the electric potential energy stored in the capacitor? (A) It doubles. (B) It is halved. (C) It remains the same. (D) It quadruples.

Free Response Question

Two point charges, $q_1 = +4 \mu C$ and $q_2 = -2 \mu C$, are placed 0.2 m apart.

(a) Calculate the electric potential energy of the system. (b) Calculate the magnitude of the electric field at the midpoint between the two charges. (c) A third charge, $q_3 = +1 \mu C$, is brought from infinity to the midpoint between $q_1$ and $q_2$. How much work is required to bring $q_3$ to this location?

Scoring Rubric

(a) (3 points) - 1 point for correctly using the formula $U = k \frac{q_1 q_2}{r}$ - 1 point for correct substitution of values - 1 point for correct answer with units: $U = (9 \times 10^9) \frac{(4 \times 10^{-6})(-2 \times 10^{-6})}{0.2} = -0.36 J$

(b) (4 points) - 1 point for recognizing that the electric field is the vector sum of the fields due to each charge - 1 point for correct formula for electric field: $E = k \frac{q}{r^2}$ - 1 point for correct substitutions for each charge - 1 point for correct answer with units: $E = 9 \times 10^9 (\frac{4 \times 10^{-6}}{0.1^2} + \frac{2 \times 10^{-6}}{0.1^2}) = 5.4 \times 10^6 N/C$

(c) (3 points) - 1 point for recognizing that work is equal to the change in potential energy: $W = q_3 \Delta V$ - 1 point for calculating the electric potential at the midpoint: $V = k(\frac{q_1}{r} + \frac{q_2}{r}) = 9 \times 10^9 (\frac{4 \times 10^{-6}}{0.1} + \frac{-2 \times 10^{-6}}{0.1}) = 1.8 \times 10^5 V$ - 1 point for correct answer with units: $W = (1 \times 10^{-6})(1.8 \times 10^5) = 0.18 J$

Alright, you've made it through! Remember, you're not just memorizing facts; you're understanding the beautiful dance of energy and charges. Go get that 5! 💪