Khan Academy — searchable YouTube transcripts & AI Q&A

Conservation of electric energy | AP Physics | Khan Academy

Electric potential energy changes can be calculated as the product of charge and potential difference, independent of path. The speaker demonstrates this with a charge moving in a uniform field, showing that energy conservation links the change in potential energy to kinetic energy, enabling speed calculations. The electron volt is introduced as a convenient unit for energy gained by a charge e accelerated through one volt, and the approach is applied to find final speeds and to reason about potential energy changes when moving charges in fields.

Connecting electric potential and field using calculus | AP Physics | Khan Academy

The electric field at a point is the negative gradient of the electric potential, which can be computed using derivatives for each spatial component. Conversely, the potential difference between two points is the negative line integral of the electric field along any path. For a uniform field, this simplifies to -E·Δr, as shown in an example where a 1000 V/m field over 5 m at 53° gives a -3000 V difference.

Electric potential of charge distributions | AP Physics | Khan Academy

Electric potential due to a continuous charge distribution is calculated by integrating the potential contributions from infinitesimal charge elements, unlike the vector sum required for electric fields. For a uniformly charged ring, the potential at the center simplifies to Q/(4πε₀R) because the distance is constant, while for a rod, the integral must account for a varying distance and charge density. The method generalizes the point-charge formula using calculus.

Electric potential and electric field | AP Physics | Khan Academy

The electric field strength indicates how much electric potential drops per meter, with the field pointing in the direction of decreasing potential. For uniform fields, this is exactly the potential drop per meter, while for non-uniform fields it represents the average over that distance. Equipotential lines or surfaces are always perpendicular to field lines, and their spacing reflects field strength: closer lines mean a stronger field.

From ROI to "Return on Learning": A District's Khan Academy Story

West Hempstead district leaders and teachers argue that Khan Academy and Khanmigo support a shift from transactional metrics like test scores to a broader 'return on learning,' which builds durable skills such as critical thinking and problem-solving. They emphasize that effective implementation depends on strong teacher training and ongoing support, and they use Khanmigo's Socratic tutoring to help students learn to ask better questions and persist through challenges. The team also stresses the importance of using AI responsibly within a 'walled garden' and modeling appropriate use, especially for younger students.