Electric Potential Difference using Integrals

Starting from the fact that the electrostatic force is conservative (F = -dU/dr), this video derives the change in electric potential energy of a charge moving through an electric field, ΔU = -∫qE·dr, then uses a hanging-charge demonstration to compare how positive and negative charges gain or lose electric potential energy relative to a mass in a gravitational field. It defines electric potential as electric potential energy per unit charge (V = U/q), derives electric potential difference as ΔV = -∫E·dr, and closes by showing that this makes volts per meter an equivalent unit for electric field, alongside newtons per coulomb. Want Lecture Notes? http://www.flippingphysics.com/electr... Chapters: 0:00 Change in Electric Potential Energy 2:30 Moving objects through fields 5:53 Electric Potential 7:04 Electric Potential Difference 8:52 Electric Field using Volts Thank you to Beth Baran and the rest of my wonderful Patreon supporters. Please consider supporting me monthly at   / flippingphysics   Thank you to Carl Hansen, Julie Langenbruner, and John Paul Nichols for being my Quality Control Team for this video. http://flippingphysics.com/quality-co... Gracias a David Figuero y Mauricio Escobar por editar las traducciones al español de este video. This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. #ElectricPotentialEnergy #ElectricPotential #Volts Curriculum Standards: AP Physics C: E&M, Unit 9 Electric Potential, Topic 9.2 Electric Potential 9.2.A.1: "Electric potential describes the electric potential energy per unit charge at a point in space." 9.2.A.3: "The electric potential difference between two points is the change in electric potential energy per unit charge when a test charge is moved between the two points." 9.2.B.1: "The value of an electric field component in any direction at a given location is equal to the negative of the spatial rate of change in electric potential at that location." 9.2.B.2: "The change in electric potential between two points can be determined by integrating the dot product of the electric field and the displacement along the path connecting the points." AP Physics C: E&M, Unit 9, Topic 9.3 Electric Potential Energy 9.3.A.1: "When a charged object moves between two locations with different electric potentials, the resulting change in the electric potential energy of the object-field system is given by the equation ΔU = qΔV." 9.3.A.2: "The movement of a charged object between two points with different electric potentials results in a change in kinetic energy of the object consistent with the conservation of energy." JEE Main Physics / NEET Physics, Unit 11: Electrostatics "Electric potential and its calculation for a point charge, electric dipole and system of charges, potential difference, equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field."