Electrical Energy and Capacitance

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 force ΔPE=Pef-Pei =- Wf Coulomb force is conservative If 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)

Work –energy theorem W=q Ex Δx =ΔKE But the work done by a conservative force can be reinterpreted as the negative of the charge in a potential energy associated with that force ΔPE 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 Δx SI unit J (Joule)

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) =0 ΔKE=mgd

Electric Potential F = qE The 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/q SI unit J/C or V (Joule/Coulomb or Volt) Electric potential is a scalar quantity

Electric potential and potential energy due to point charges The electric field of a point charge extends throughout space, so its electrical potential also Electric potential created by a point charge: V=ke q/r The 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

Potentials and charged conductors The electric potential at all points on a charged conductor W= -ΔPE =-q( VB-VA) No net work is required to move a charge between two points that are at the same electric potential All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential

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 surface The electron volt is defined as KE that an electron gains when accelerated through a potential difference of 1V 1eV =1.6x 10-19 C V =1.6x10-19 J

Equipotential surface is a surface on which all points are at the same potential The electric field at every point of an equipotential surface is perpendicular to the surface.

Capacitance A capacitor- is a device used in variety of electric circuits The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor (plate) to the manitude