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

• ΔKE = ΙqΙ E d

• 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