Back to Electric Potential

Lesson PreviewLesson 1 of 3 in this unit

9.1 Electric Potential Energy

Part of Electric Potential in AP® Physics C: Electricity and Magnetism. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

Start free

The electric potential energy UE{U_E} of a charge at point a{a} is defined as −W{-W} where W{W} is the work done to move the charge from infinity to point a{a}. In general, ΔUE=−∫F⃗⋅ds⃗{\Delta U_E = -\int \vec{F} \cdot d\vec{s}}, where s{s} is the path the charge takes and F⃗{\vec{F}} is the electric force acting on the charge. By convention, the force acting on a charge "at infinity" is defined to be 0. We can use this convention to find the potential energy of a charge at point a{a}: dUE=−F⃗⋅dr⃗{dU_E = -\vec{F} \cdot d\vec{r}} where r{r} is the distance between the source charge q1{q_1} and the moving charge q2{q_2}. Evaluating this integral lends

∫∞a−F⃗⋅dr⃗=∫a∞F⃗⋅dr⃗=∫a∞q1q24πϵ0r2r^⋅dr⃗=q1q24πϵ0a=kq1q2a\int_{\infty}^{a} -\vec{F} \cdot d\vec{r} = \int_{a}^{\infty} \vec{F} \cdot d\vec{r} = \int_{a}^{\infty} \frac{q_1 q_2}{4\pi\epsilon_0 r^2} \hat{r} \cdot d\vec{r} = \frac{q_1 q_2}{4\pi\epsilon_0 a} = \frac{k q_1 q_2}{a}

In this unit

3 lessons

  1. 9.1Electric Potential EnergyThis lesson
  2. 9.2Electric PotentialPreview lesson
  3. 9.3Conservation of Electric EnergyPreview lesson

Continue the full lesson in Stellar

Create a free account to unlock the remaining sections, checkpoints, course practice, and progress tracking for AP® Physics C: Electricity and Magnetism.

Start free