---
title: "AP Physics 2 10.7: Conservation of Electric Energy"
description: "Review AP Physics 2 10.7, including conservation of electric energy, electric potential energy, Delta U_E = q Delta V, Delta K = -Delta U_E, potential difference, charged particles, kinetic energy changes, sign conventions, electrons, protons, and energy bar chart reasoning."
canonical: "https://fiveable.me/ap-physics-2-revised/unit-10/7-conservation-of-electric-energy/study-guide/xeLRWRG6zabL3Yw4"
type: "study-guide"
subject: "AP Physics 2"
unit: "Unit 10 – Electric Force, Field, and Potential"
lastUpdated: "2026-06-09"
---

# AP Physics 2 10.7: Conservation of Electric Energy

## Summary

Review AP Physics 2 10.7, including conservation of electric energy, electric potential energy, Delta U_E = q Delta V, Delta K = -Delta U_E, potential difference, charged particles, kinetic energy changes, sign conventions, electrons, protons, and energy bar chart reasoning.

## Guide

When a charged object moves between two points with different electric potentials, its electric potential energy changes by $\Delta U_E = q \Delta V$. Because energy is conserved, that change in [potential energy](/ap-physics-2-revised/key-terms/potential-energy "fv-autolink") shows up as a change in [kinetic energy](/ap-physics-2-revised/key-terms/kinetic-energy "fv-autolink"), which is how charged particles speed up or slow down in electric fields.

## Why This Matters for the AP Physics 2 Exam

This topic ties electric potential to motion using [conservation of energy](/ap-physics-2-revised/key-terms/conservation-of-energy "fv-autolink"), a tool you already used in mechanics. On the exam you may need to predict how a charge's kinetic energy changes as it moves through a [potential difference](/ap-physics-2-revised/key-terms/electric-potential-difference "fv-autolink"), and explain why using energy bar charts, equations, and clear reasoning.

[Unit 10](/ap-physics-2-revised/unit-10 "fv-autolink") content is strong practice for the free-response question that asks you to translate between representations. You might sketch [equipotential lines](/ap-physics-2-revised/key-terms/equipotential-lines "fv-autolink"), build energy bar charts for a charge released near a charged object, and then explain how those representations agree with the math. Getting comfortable with $\Delta U_E = q \Delta V$ and energy conservation helps you connect a verbal description, a diagram, and an equation for the same situation.

## Key Takeaways

- The change in electric potential energy for a charge moving between two potentials is $\Delta U_E = q \Delta V$, measured in joules.
- Track signs carefully: $q$ can be positive or negative, and $\Delta V = V_{final} - V_{initial}$ can be positive or negative.
- Energy is conserved, so a drop in electric potential energy becomes an increase in kinetic energy: $\Delta K = -\Delta U_E$.
- Positive charges speed up when moving toward lower potential; negative charges speed up when moving toward higher potential.
- The electric field points toward decreasing potential, so use the field, not just terminal labels, to decide which way a charge accelerates.
- For a particle starting from rest, the kinetic energy gained equals the magnitude of $q \Delta V$, which lets you solve for final speed.

## Changes in Energy Due to Electric Potential Difference

### Electric Potential Energy Changes

When a charged object moves through an electric field, its electric potential energy changes. This is similar to how an object's gravitational potential energy changes when it moves up or down in Earth's gravitational field.

- The change in electric potential energy is directly proportional to both the charge of the object and the potential difference between the two locations.
- This relationship is written as: $$\Delta U_E = q \Delta V$$
  - $\Delta U_E$ is the change in electric potential energy (in joules)
  - $q$ is the charge of the object (in coulombs)
  - $\Delta V$ is the electric potential difference (in volts)
- The sign of the energy change depends on the sign of the charge and the direction of movement.
  - Positive charges gain potential energy when moving to higher potential.
  - Negative charges gain potential energy when moving to lower potential.

For example, when an [electron](/ap-physics-2-revised/unit-15/2-the-bohr-model-of-atomic-structure/study-guide/gzEFr1ron8hpACPx "fv-autolink") ([negative charge](/ap-physics-2-revised/key-terms/negative-charge "fv-autolink")) moves from a lower electric potential to a higher electric potential, its electric potential energy decreases because $\Delta U_E = q\Delta V$ and $q$ is negative. The direction the electron naturally accelerates depends on the electric field, not just on the terminal labels. A proton pushed toward another proton gains electric potential energy as it moves against the repulsive force.

### Conservation of Energy Principle

Energy cannot be created or destroyed, only transformed from one form to another. This principle governs how charged particles behave in electric fields.

When a charged particle moves between points with different electric potentials:
- The change in kinetic energy equals the negative of the change in electric potential energy.
- This is written as: $$\Delta K = -\Delta U_E = -q\Delta V$$
- The total mechanical energy of the object-field system stays constant: $$\Delta K + \Delta U_E = 0$$

This shows up in many electrical situations:

- An electron accelerating in an electric field converts electric potential energy into kinetic energy.
- A proton slowing down as it approaches another proton converts kinetic energy into electric potential energy.
- In a [circuit](/ap-physics-2-revised/unit-11/2-simple-circuits/study-guide/LROjr9EJ6hjfPDMC "fv-autolink"), the electric potential energy of the charge-field system can be transformed into other forms such as [thermal energy](/ap-physics-2-revised/unit-11/3-resistance-resistivity-and-ohms-law/study-guide/y0ZmKqhOPqeLWZFa "fv-autolink"), light, or sound as charges move through circuit elements.

This idea is central to understanding charged particles in accelerators, cathode ray tubes, and other devices where charges move through potential differences.

## How to Use This on the AP Physics 2 Exam

### Problem Solving

- Start by writing $\Delta V = V_{final} - V_{initial}$ before plugging into $\Delta U_E = q \Delta V$. Sign mistakes here cause most wrong answers.
- Use $\Delta K = -\Delta U_E$ to connect potential energy changes to speed changes.
- For a charge starting from rest, set $\frac{1}{2}mv^2 = |q \Delta V|$ and solve for $v$.

### Free Response

- When asked to translate between representations, line up three views of the same scenario: a diagram (equipotential lines or field vectors), an energy bar chart, and the equation $\Delta U_E = q \Delta V$.
- In energy bar charts, show that any decrease in electric potential energy matches an increase in kinetic energy so the bars stay consistent with conservation of energy.
- When you explain your reasoning, state the sign of the charge, the sign of $\Delta V$, and what that means for kinetic energy.

### Common Trap

- Do not assume a charge always speeds up when moving to higher potential. That is only true for positive charges. Negative charges speed up moving toward higher potential because $q$ is negative.

## Practice Problem 1: Electric Potential Energy Change

> A proton (charge = +1.6 × 10^-19 C) moves from a point where the electric potential is +200 V to a point where the electric potential is +50 V. Calculate the change in the proton's electric potential energy and determine whether the proton gains or loses kinetic energy during this movement.

**Solution**

Use $$\Delta U_E = q\Delta V$$.

Identify the values:
- Charge of proton, q = +1.6 × 10^-19 C
- Initial potential, V₁ = +200 V
- Final potential, V₂ = +50 V

The change in potential is:
$$\Delta V = V_2 - V_1 = 50\text{ V} - 200\text{ V} = -150\text{ V}$$

Now calculate the change in electric potential energy:
$$\Delta U_E = q\Delta V = (1.6 \times 10^{-19}\text{ C})(-150\text{ V}) = -2.4 \times 10^{-17}\text{ J}$$

Since the change in electric potential energy is negative, the proton loses electric potential energy. By conservation of energy, its kinetic energy increases by the same amount. The proton gains 2.4 × 10^-17 J of kinetic energy as it moves from the higher potential to the lower potential.

## Practice Problem 2: Conservation of Energy

> An electron (mass = 9.11 × 10^-31 kg, charge = -1.6 × 10^-19 C) is initially at rest at a point where the electric potential is 0 V. It then moves to a point where the electric potential is +5000 V. Calculate the final speed of the electron.

**Solution**

Use conservation of energy. The change in kinetic energy equals the negative of the change in electric potential energy.

Identify the values:
- Mass of electron, m = 9.11 × 10^-31 kg
- Charge of electron, q = -1.6 × 10^-19 C
- Initial potential, V₁ = 0 V
- Final potential, V₂ = +5000 V
- Initial [velocity](/ap-physics-2-revised/key-terms/velocity "fv-autolink"), v₁ = 0 (electron starts at rest)

The change in electric potential energy is:
$$\Delta U_E = q\Delta V = q(V_2 - V_1) = (-1.6 \times 10^{-19}\text{ C})(5000\text{ V} - 0\text{ V}) = -8.0 \times 10^{-16}\text{ J}$$

Since energy is conserved, this decrease in electric potential energy results in an equal increase in kinetic energy:
$$\Delta K = -\Delta U_E = 8.0 \times 10^{-16}\text{ J}$$

The final kinetic energy is:
$$K_2 = K_1 + \Delta K = 0 + 8.0 \times 10^{-16}\text{ J} = 8.0 \times 10^{-16}\text{ J}$$

Using $$K = \frac{1}{2}mv^2$$, solve for the final velocity:
$$v_2 = \sqrt{\frac{2K_2}{m}} = \sqrt{\frac{2(8.0 \times 10^{-16}\text{ J})}{9.11 \times 10^{-31}\text{ kg}}} = 4.2 \times 10^7\text{ m/s}$$

The electron reaches a speed of about 4.2 × 10^7 m/s after accelerating through the potential difference.

## Common Misconceptions

- "Higher potential always means more energy for a charge." Only for positive charges. For a negative charge, $\Delta U_E = q \Delta V$ is negative when $\Delta V$ is positive, so its potential energy drops.
- "A charge always moves toward lower potential." Particles move based on the force from the field. Positive charges tend toward lower potential, but negative charges tend toward higher potential.
- "Kinetic energy gained equals $\Delta V$." Kinetic energy gained equals the magnitude of $q \Delta V$, not $\Delta V$ by itself. You must include the charge.
- "Forgetting the sign of $\Delta V$." Always compute $\Delta V = V_{final} - V_{initial}$. Reversing this flips the sign of your energy change.
- "Electric potential energy and electric potential are the same thing." Potential energy ($U_E$) depends on the charge moved; potential ($V$) is energy per unit charge and does not depend on a [test charge](/ap-physics-2-revised/key-terms/test-charge "fv-autolink") being present.

## Related AP Physics 2 Guides

- [10.1 Electric Charge and Electric Force](/ap-physics-2-revised/unit-10/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1)
- [10.2 The Process of Charging](/ap-physics-2-revised/unit-10/2-the-process-of-charging/study-guide/fQJqVklZDhbQdyBa)
- [10.3 Electric Fields](/ap-physics-2-revised/unit-10/3-electric-fields/study-guide/I5lSNgudkyVNrR1L)
- [10.5 Electric Potential](/ap-physics-2-revised/unit-10/5-electric-potential/study-guide/NNaK6pYgyfxnT9Ma)
- [10.6 Capacitors](/ap-physics-2-revised/unit-10/6-capacitors/study-guide/BalONZFM1MOIxU84)
- [10.4 Electric Potential Energy](/ap-physics-2-revised/unit-10/4-electric-potential-energy/study-guide/XB2Mvgn54KTHVQj6)

## Vocabulary

- **charged object**: An object that possesses electric charge and can interact with electric and magnetic fields.
- **conservation of energy**: The principle that the total energy in an isolated system remains constant, with energy transforming between different forms but not being created or destroyed.
- **electric potential**: A scalar quantity that represents the electric potential energy per unit charge at a point in space, measured in volts.
- **electric potential energy**: The energy stored in a system due to the position of a charged object in an electric field, dependent on the charge and electric potential.
- **kinetic energy**: The energy of motion possessed by an object due to its velocity.

## FAQs

### What is conservation of electric energy in AP Physics 2?

Conservation of electric energy means that when a charged object moves through a potential difference, electric potential energy and kinetic energy transform into each other while total energy is conserved.

### What does Delta U_E = q Delta V mean?

Delta U_E = q Delta V gives the change in electric potential energy for a charge q moving through a potential difference Delta V. The sign depends on both the charge and whether the final potential is higher or lower.

### How is kinetic energy related to electric potential energy?

If only electric forces do work, the change in kinetic energy is the negative of the change in electric potential energy: Delta K = -Delta U_E. A decrease in electric potential energy becomes an increase in kinetic energy.

### Do positive and negative charges speed up in the same direction?

No. Positive charges naturally speed up toward lower electric potential, while negative charges naturally speed up toward higher electric potential. Always track the sign of the charge.

### How do you solve electric potential energy practice problems?

Start with Delta V = V_final - V_initial, then use Delta U_E = q Delta V. Connect energy changes with Delta K = -Delta U_E, and for a particle starting from rest use kinetic energy to solve for speed.

### What is a common mistake with electric potential energy?

A common mistake is assuming all charges speed up toward higher potential. That is true for negative charges but not positive charges, because q changes the sign of Delta U_E.

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