zuai-logo

Electric Potential Energy

Elijah Ramirez

Elijah Ramirez

8 min read

Listen to this study note

Study Guide Overview

This study guide covers electric potential energy in AP Physics C: E&M. It explains the definition of electric potential energy, its relationship to work, and how to calculate it for two-charge and multiple-charge systems using the superposition principle. The guide also connects the concept to the work-energy theorem, electric potential (voltage), and conservation of energy, and provides practice questions with solutions.

AP Physics C: E&M - Electric Potential Energy Study Guide

Hey there! Let's get you prepped and confident for your AP Physics C: E&M exam. We're diving into electric potential energy, a key concept that shows up everywhere on the test. Think of this as your ultimate cheat sheet for tonight.

Electric Potential Energy: The Basics

Electric potential energy is all about the energy stored in a system of charged particles because of their electric field interactions. It's like the potential a stretched spring has to do work. The closer like charges are, the more potential energy they have, and the opposite is true for opposite charges.

  • Definition: Energy stored in a system of charges due to their positions and interactions.

  • Key Idea: Work is required to bring like charges together and to separate opposite charges. This work is stored as potential energy.

Work and Potential Energy

  • Work-Energy Connection: The work done by an external force to move charges into their current arrangement is equal to the electric potential energy stored in the system.

  • Analogy: Imagine lifting a book against gravity. You do work, and the book gains gravitational potential energy. Similarly, when you move charges around, you're doing work, and the system gains electric potential energy.

  • Release: When charges move to a lower potential energy configuration, this stored energy is released (like a book falling).

Calculating Electric Potential Energy

Key Concept

Two-Charge Systems

  • Formula: The electric potential energy (UEU_E) between two point charges is given by:

UE=kq1q2rU_{E} = k \frac{q_1 q_2}{r}

Where: - UEU_E is the electric potential energy (in Joules, J) - q1q_1 and q2q_2 are the magnitudes of the charges (in Coulombs, C) - rr is the distance between the charges (in meters, m) - kk is Coulomb's constant (8.99×109N⋅m2C28.99 \times 10^9 \frac{\text{N} \cdot \text{m}^2}{\text{C}^2})

  • Inverse Relationship: Notice the 1r\frac{1}{r} term. This means that: - Potential energy decreases as the distance between the charges increases. - Doubling the distance halves the potential energy.

  • Sign Matters: - Like charges (both positive or both negative) have a positive UEU_E (they repel each other). - Opposite charges have a negative UEU_E (they attract each other).

Memory Aid

Memory Aid: Remember, like charges repel, and opposites attract. Positive energy means they're fighting to stay together, and negative means they're happy to be together!

Key Concept

Multiple-Charge Systems

  • Superposition Principle: For more than two charges, you calculate the potential energy for every pair of charges and add them up.

  • Step-by-Step: 1. Calculate UEU_E for each pair of charges using the formula above. 2. Add all the individual potential energies together.

  • Total Potential Energy: This sum gives the total electric potential energy stored in the entire system.

  • Scalar Nature: Electric potential energy is a scalar, so you add the values directly (no need to worry about components!). 💡

  • Important Note: Make sure you consider every unique pair of charges. Don't double-count interactions!

Two positive charges Caption: Two positive charges experience a repulsive force, and the system has positive potential energy.

Two opposite charges Caption: Two opposite charges experience an attractive force, and the system has negative potential energy.

Connections to Other Concepts

  • Work-Energy Theorem: The change in electric potential energy is related to the work done by the electric force. This connection is crucial for solving many problems.

  • Electric Potential (Voltage): Electric potential energy is closely related to electric potential (voltage). Voltage is potential energy per unit charge. V=U/qV = U/q

  • Conservation of Energy: In a closed system, the total energy (kinetic + potential) remains constant. This is your go-to principle for many complex problems.

Exam Tip

Always check the signs of your charges and potential energies. A common mistake is forgetting that opposite charges result in negative potential energy.

Final Exam Focus

  • High Priority Topics: - Calculating potential energy for two-charge and multi-charge systems. - Understanding the relationship between work, potential energy, and electric force. - Applying conservation of energy to solve problems involving charged particles.

  • Common Question Types: - Multiple Choice: Conceptual questions about potential energy, work, and the signs of charges. - Free Response: Problems that require calculating potential energy for multiple charges and applying conservation of energy.

  • Last-Minute Tips: - Time Management: Don't spend too long on any one question. If you're stuck, move on and come back later. - Common Pitfalls: Watch out for sign errors. Pay close attention to units and conversions. - Strategies: Draw diagrams to visualize the problem. Write down all given information and the relevant formulas. - Stay Calm: You've got this! Take a deep breath and trust your preparation.

Common Mistake

A common mistake is forgetting to include all pairs of charges when calculating total potential energy in a system. Always double-check that you haven't missed any interactions.

Practice Questions

Practice Question

Multiple Choice Questions:

  1. Two point charges, +q and -q, are initially a distance r apart. If the distance between them is doubled to 2r, what happens to the electric potential energy of the system? (A) It is doubled. (B) It is halved. (C) It remains the same. (D) It is quadrupled. (E) It is quartered.

  2. Three identical point charges, each with a charge +q, are placed at the corners of an equilateral triangle. Which of the following is true about the total electric potential energy of the system? (A) It is zero. (B) It is positive. (C) It is negative. (D) It depends on the size of the triangle. (E) It depends on the value of q.

Free Response Question:

Three point charges are arranged as shown in the figure below. Charge q1=+2μCq_1 = +2\mu C is located at (0, 0), charge q2=−3μCq_2 = -3\mu C is located at (4 m, 0), and charge q3=+4μCq_3 = +4\mu C is located at (0, 3 m).

Charge configuration

(a) Calculate the electric potential energy of the system of three charges.

(b) How much work is required to bring a fourth charge, q4=−1μCq_4 = -1\mu C, from infinity to the point (4 m, 3 m)?

(c) What is the total potential energy of the system with all four charges?

Scoring Rubric:

(a) Calculating the potential energy of the three-charge system: - 1 point: Correctly using the formula for potential energy between two charges. - 1 point: Correctly calculating the potential energy between q1q_1 and q2q_2. - 1 point: Correctly calculating the potential energy between q1q_1 and q3q_3. - 1 point: Correctly calculating the potential energy between q2q_2 and q3q_3. - 1 point: Correctly summing the three potential energies.

(b) Calculating the work needed to bring a fourth charge: - 1 point: Recognizing that work done equals the change in potential energy. - 1 point: Correctly calculating the potential energy between q4q_4 and q1q_1. - 1 point: Correctly calculating the potential energy between q4q_4 and q2q_2. - 1 point: Correctly calculating the potential energy between q4q_4 and q3q_3. - 1 point: Correctly summing the potential energies to find the work done.

(c) Calculating the total potential energy of the four-charge system: - 1 point: Correctly summing the potential energy of the original three charges (from part a) with the potential energy of the fourth charge (from part b).

Answers:

Multiple Choice:

  1. (B) It is halved.
  2. (B) It is positive.

Free Response:

(a) Utotal=U12+U13+U23U_{total} = U_{12} + U_{13} + U_{23}

U12=kq1q2r12=(8.99×109)(2×10−6)(−3×10−6)4=−0.0135JU_{12} = k \frac{q_1 q_2}{r_{12}} = (8.99 \times 10^9) \frac{(2 \times 10^{-6})(-3 \times 10^{-6})}{4} = -0.0135 J

U13=kq1q3r13=(8.99×109)(2×10−6)(4×10−6)3=0.024JU_{13} = k \frac{q_1 q_3}{r_{13}} = (8.99 \times 10^9) \frac{(2 \times 10^{-6})(4 \times 10^{-6})}{3} = 0.024 J

U23=kq2q3r23=(8.99×109)(−3×10−6)(4×10−6)5=−0.0216JU_{23} = k \frac{q_2 q_3}{r_{23}} = (8.99 \times 10^9) \frac{(-3 \times 10^{-6})(4 \times 10^{-6})}{5} = -0.0216 J

Utotal=−0.0135+0.024−0.0216=−0.0111JU_{total} = -0.0135 + 0.024 - 0.0216 = -0.0111 J

(b) W=ΔU=Uf−Ui=Uf−0=UfW = \Delta U = U_f - U_i = U_f - 0 = U_f

U14=kq1q4r14=(8.99×109)(2×10−6)(−1×10−6)5=−0.0036JU_{14} = k \frac{q_1 q_4}{r_{14}} = (8.99 \times 10^9) \frac{(2 \times 10^{-6})(-1 \times 10^{-6})}{5} = -0.0036 J

U24=kq2q4r24=(8.99×109)(−3×10−6)(−1×10−6)3=0.009JU_{24} = k \frac{q_2 q_4}{r_{24}} = (8.99 \times 10^9) \frac{(-3 \times 10^{-6})(-1 \times 10^{-6})}{3} = 0.009 J

U34=kq3q4r34=(8.99×109)(4×10−6)(−1×10−6)4=−0.009JU_{34} = k \frac{q_3 q_4}{r_{34}} = (8.99 \times 10^9) \frac{(4 \times 10^{-6})(-1 \times 10^{-6})}{4} = -0.009 J

W=U14+U24+U34=−0.0036+0.009−0.009=−0.0036JW = U_{14} + U_{24} + U_{34} = -0.0036 + 0.009 - 0.009 = -0.0036 J

(c) Utotal=−0.0111−0.0036=−0.0147JU_{total} = -0.0111 - 0.0036 = -0.0147 J

You've got this! Go ace that exam!

Explore more resources

FlashcardFlashcard

Flashcard

Continute to Flashcard

Question BankQuestion Bank

Question Bank

Continute to Question Bank

Mock ExamMock Exam

Mock Exam

Continute to Mock Exam

Previous Topic - Gauss's LawNext Topic - Electric Potential

Question 1 of 9

What is the fundamental concept behind electric potential energy? 🤔

Energy of moving charges in a magnetic field

Energy stored in a system of charges due to their positions and interactions

Kinetic energy of electrons in a circuit

Energy released when charges are grounded