Electric Potential Energy A charge q in an electric field behaves similarly to a mass m in a gravitational field. The electric force F = qE is conservative. Change in potential energy from position a to b : ΔU is independent of the path from position a to b :

Electric Potential The electric field is related to how fast the potential is changing: For a constant electric field:

Electric Potential and Potential Difference Electric Potential: Electric potential difference ΔV between a and b :

Electric Potential and Potential Energy Electric potential V has units of Joules/Coulomb which is defined as a Volt: 1 Volt = 1 Joule/Coulomb One Joule is the work done in moving one Coulomb of charge through a potential difference of one Volt. Electric field has units of Newtons/Coulomb or Volts/meter: 1N/C = 1 J/(mC) = 1 V/m Difference in potential energy Difference in electric potential

Analogy between Electric and Gravitational Fields d m m q q EG ΔU = qΔV = - qEd ΔU = - mgd The charge and mass lose potential energy and gain kinetic energy when they move in the direction of the field.

Kinetic Energy of a Charge Accelerated by an Electric Field The kinetic energy acquired by an electron or a proton accelerated through a potential difference of 1000 Volts: U ba = qV ba = (1.60 x C)(1000 V) = 1.60 x J = 1000 eV (electron volts) = 1 keV (kilo electron volt)  One electron-volt (1 eV) is the kinetic energy gained by an elemental charge (electron or proton) when it is accelerated through a potential difference of one Volt. 1 eV = 1.6 x J

Electric Potential Energy: The Electron Volt Suppose a point charge q is moved between two points a and b in space, where the electric potentials due to other charges are V a and V b. The change in potential energy is: ΔU = U b – U a = q(V b – V a ) = qV ba Unit = Electron Volt (eV): 1 eV = 1.6 x J e.g. a proton accelerated through a potential difference of 200 kV acquires a kinetic energy of 200 keV (losing 200 keV of electric potential energy).

Electric Potential due to Point Charge Electric Field: Convention: V=0 at infinite r Using Calculus, it can be shown

Electric Potential due to a Point Charge Electric potential at a distance r from a positive charge Q Electric potential at a distance r from a negative charge Q

Equipotential Surfaces Equipotential surfaces are surfaces of constant electric potential (just as lines of constant elevation on a topological map are lines of constant gravitational potential). Equipotential surfaces are always perpendicular to the direction of the electric field. (just as the “fall line” is perpendicular to the contour lines on a topological map). Charged Parallel Plates Two Equal and Opposite Charges