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. Work done Fx cos qEs cos Change in potential energy from position a to b: U U b U a qEs cos UU 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 Ua Va (scalar quantity) Electric Potential: q - independent of q Electric potential - depends on position a difference V between a and b:
Ub U a V Vb Va q q U E x x is along field lines q Electric Potential and Potential Energy U U b U a qVb Va Difference in potential energy
Difference in electric potential 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 Analogy between Electric and Gravitational Fields q
E m G d q m U = qV = - qEd U = - 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: Uba = qVba = (1.60 x 10-19 C)(1000 V) = 1.60 x 10-13 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 10-19 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 Va and Vb. The change in potential energy is: UU = Ub Ua = q(Vb Va) = qVba Unit = Electron Volt (eV): 1 eV = 1.6 x 10-19 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: Q E k 2 (radially outward) r Using Calculus, it can be shown 1 1 V Vb Va kQ rb ra Convention: V=0 at infinite r Q
V k (electric potential) r 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 Charges Two Equal and Opposite
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