1. Electrical Energy and Capacitance

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 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)

4. 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)

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) =0
ΔKE=mgd

7. 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

8. 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

11. 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

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

16. 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.

18. 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