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Conservation of Electric Energy

AP Course

AP Physics C: Electricity and Magnetism

Updated for the AP Physics C: Electricity and Magnetism framework effective fall 2024, with calculus-based fields, circuits, and induction.

Build calculus-based E&M with original field models, derivations, experiments, quizzes, and practice sets.

AP Physics C: Electricity and Magnetism · Unit 9 · Topic 9.3

Conservation of Electric Energy

Scalar potential and vector field are linked by line integrals and gradients, simplifying energy and distribution problems.

Inverse relationship · Conservation of Electric EnergyThe response falls nonlinearly as the independent variable increases; use the governing equation for exact scaling.

1. Topic Lens

Conservation of Electric Energy is studied through electric potential. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[\Delta V=-\int_i^f\vec E\cdot d\vec\ell\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. Electric potential change is negative work per unit charge done by the field.
  2. For an infinitesimal displacement, dV=-E·dℓ.
  3. The directional-derivative identity for every direction gives E=-∇V.
\[\vec E=-\nabla V\]

3. Detailed Visual Model

Conservation of Electric EnergyTopic-matched fine pixel-art model · use the lesson's equations and labeled diagrams for exact scientific meaning.

4. Worked Example and Lab Link

A charge q=2 C moves through ΔV=-5 V. Find its potential-energy change.

Answer: ΔU=qΔV=(2)(-5)=-10 J.

Investigation idea: Create a numerical potential map for multiple charges and compare gradient arrows with directly summed fields.

Common trap: Potential can be zero where field is not zero; potential reference choice does not change measurable differences.

Checkpoint · Topic 9.3

Explain how conservation of electric energy supports or limits this conclusion: ΔU=qΔV=(2)(-5)=-10 J.

Official curriculum reference: College Board AP Physics C: Electricity and Magnetism course page. The explanation and worked example are independently written for this study site.