electric field

• Electric charge is a fundamental property of matter with two types: positive and negative
• Two bodies with the same type of charge repulse each other, while opposite charges attract
• The electric charge is always a multiple of the elementary charge, e = 1.602177 x 10^-19 C, which is the charge on an electron
• In all natural processes, the total or net charge of an isolated system remains constant
• Coulomb’s law expresses the electric force F exerted by a point charge q on another point charge q’ as F = K e q q’ / r^2, where r is the distance between the charges and K e = 9 × 10^9 N C^-2m^2
• The electric field E generated by a charge distribution is the force F exerted by the distribution on a test particle divided by the charge q of the test particle
• The electric field lines start at positive charges and end at negative charges; a uniform field has the same intensity and direction at all points in space
• The electric potential energy of a test particle in the field created by fixed particles is given by Ep = K e q q i / r i, where the electric potential V = Ep / q
• The potential difference ∆V between two points is related to the work W done by the electric field, given by ∆V = V2 - V1 = - E ⋅ dl
• The relation between electric field E and electric potential V is given by dV = -E ⋅ dl
• Equipotential surfaces have the same electric potential at their points, with field lines perpendicular to them
• Gauss’s law states that the total electric flux through any closed surface is equal to the total (net) electric charge inside the surface divided by ε0
• Calculation of electric field using Gauss’s law:

  • Gauss’s law may be used to find the electric field produced by highly symmetrical charge distributions such as infinite lines, planes or spheres
  • The crucial step in this process is to select the Gaussian surface
• Properties of conductors in electrostatic equilibrium:

  • The electric field inside a conductor in electrostatic equilibrium is zero
  • The net electric charge of a conductor in electrostatic equilibrium is found on its surface
  • The electric field on the surface of a conductor in electrostatic equilibrium is perpendicular to the surface
  • The surface of a conductor in electrostatic equilibrium is an equipotential surface
• Electric field in the proximities of a conductor in electrostatic equilibrium:

  • The electric field at points near the surface of a conductor is perpendicular to the surface and is given by E = σ / ε0, known as Coulomb's theorem
  • The field created by the total charge of the conductor is the sum of the field created by a small disk of area dS and that created by the rest of the conductor
• Conductors in an electric field:

  • When a conductor is placed in an electric field, the field inside the conductor must be cancelled for the conductor to be in electrostatic equilibrium
  • This results in the charges in the conductor being reordered to create an electric field inside the conductor to compensate the applied electric field
• Dielectric breakdown and the point effect:

  • Many non-conducting materials are ionized in very high electric fields and become conductors, known as dielectric breakdown
  • The dielectric limit of an insulator is the maximum electric-field magnitude, Emax, that can exist in this material without producing dielectric breakdown
• Capacitance:

  • A conductor with charge Q and potential V has a capacitance given by C = Q / V
• Capacitors:

  • A capacitor is an electric device used in circuits to store charge and electric energy
  • The capacitance of a capacitor is given by C = Q / ΔV, measured in farads (1 F = 1 C/V)
• Capacitors in series and parallel:

  • The equivalent capacitance of various capacitors connected together in series or parallel
• Electrostatic energy:

  • The potential electric energy U stored in a charged capacitor is calculated as the work required to charge it
  • The electric energy density uE in the space occupied by the field (in a vacuum) is given by uE = 1 / 2 ε0E^2
• Dielectrics:

  • Electrostatic properties of dielectrics
  • When a dielectric is placed within the housing of a capacitor, the capacitance increases