2 Potential difference and electrical potential Work and potential energy:Potential energy is a scalar quantity with charge to the negative of the work done by the conservative forceΔPE=Pef-Pei =- WfCoulomb force is conservativeIf imagine a small + charge placed in a uniform electric field E. As the charge moves from A to B, the work done on the charge by the electric field:W=FxΔx =q Ex (xf-xi)
4 Work –energy theoremW=q Ex Δx =ΔKEBut the work done by a conservative force can be reinterpreted as the negative of the charge in a potential energy associated with that forceΔPE of a system consisting on an object of charge q through a displacement Δx in a constant electric field E is given by:ΔPE =-WAB= -q Ex ΔxSI unit J (Joule)
6 Δ KE + ΔPE el = ΔKE +(0-ΙqΙ E d =0 Similarly , KE equal in magnitude to the loss of gravitational potential energy:ΔKE +ΔPEg =ΔKE +(0 –mgd) =0ΔKE=mgd
7 Electric PotentialF = qEThe electric potential difference between points A and B is the charge in electric potential energy as a charge q moves from A to B, divided by the charge q: ΔV =VA-VB = ΔPE/qSI unit J/C or V (Joule/Coulomb or Volt)Electric potential is a scalar quantity
8 Electric potential and potential energy due to point charges The electric field of a point charge extends throughout space, so its electrical potential alsoElectric potential created by a point charge: V=ke q/rThe electric potential of two or more charges is obtained by applying the superposition principle: the total electric potential at some point P due to several point charges is the algebraic sum of the V due to the individual charges
11 Potentials and charged conductors The electric potential at all points on a charged conductorW= -ΔPE =-q( VB-VA)No net work is required to move a charge between two points that are at the same electric potentialAll points on the surface of a charged conductor in electrostatic equilibrium are at the same potential
12 The electric potential is a constant everywhere on the surface of a charged conductor The electric potential is constant everywhere inside a conductor and equal to the same value at the surfaceThe electron volt is defined as KE that an electron gains when accelerated through a potential difference of 1V1eV =1.6x C V =1.6x10-19 J
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