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Summary

  • The quantitative expression for the effect of an electric charge and distance on electric force is given by Coulomb’s law, which states that the force between two charges is,
     
    Description: 214878.png
  • If there are a number of charges Q1, Q2, …, Qn placed at points with position vectors Description: 214870.png respectively then the resultant force Description: 214863.pngon a charge Q located at point Description: 214854.pngis,
     
    Description: 214846.png
     
    This is known as principle of superposition of charges.
  • The electric field intensity Description: 214839.png is defined as the force per unit charge when placed in an electric field. So, for a point charge, the field intensity is,
  • Description: 214829.png 
  • If there are a number of charges q1, q2, …, qn placed at points with position vectors Description: 214821.pngrespectively then the electric field intensity is,
     
    Description: 214812.png
     
    This is known as principle of superposition of field.
  • The electric field intensity due to different continuous charge distribution is given as,
     
    Description: 214803.png
  • The electric flux density Description: 214794.png is defined as the total number of electric field lines per unit area passing through the area perpendicularly (in C/m2). It is related to the field intensity as,
     
    Description: 214787.png
     
    Hence, electric flux through a surface is given as,
     
    Description: 214779.png
  • Electric field lines are the imaginary lines drawn in such a way that at every point, a line has the direction of the electric field Description: 214771.png.
  • Electric flux lines are the imaginary lines drawn in such a way that at every point, a line has the direction of the electric flux density vector Description: 214763.png.
  • Gauss’ law states that the total electric displacement or electric flux through any closed surface surrounding charges is equal to the net positive charge enclosed by that surface.
     
    Mathematically, it is expressed as,
     
    Description: 214755.png, integral form
     
    Description: 214747.png, differential form
  • The total work done in moving a unit positive charge from a point A to another point B is called the potential difference between the two points, given as,
     
    Description: 214737.png
     
    This potential difference between the points A and B is also considered to be the potential (or absolute potential) of B with respect to the potential (or absolute potential) of A. In case of a point charge, the reference is taken to be at infinity with zero potential.
  • Potential (or absolute potential) of a point is defined as the work done to bring a unit positive charge from infinity to that point. This is given as,
     
    Description: 214729.png
  • If there is a number of point charges Q1, Q2, …, Qn, located at position vectors Description: 214720.png respectively then the potential at the point Description: 214712.png is given as,
     
    Description: 214703.png
     
    This is known as principle of superposition of potential.
  • The electric potential due to different continuous charge distribution is given as,
     
    Description: 214696.png
  • The rate of change of potential with respect to the distance is called the potential gradient. The relation between the potential and field intensity is written as,
     
    Description: 214687.png
  • The surface obtained by joining the points with equal potential is known as equipotential surface.
  • Two equal and opposite point charges separated by a distance constitute an electric dipole.
  • For an electric dipole with dipole moment Description: 219640.png and centred at a position vector Description: 214680.png, the potential at a point P(rθφ) is given as,
     
    Description: 214672.png
  • Similarly, for an electric dipole with dipole moment Description: 214663.png and centred at the origin, the field intensity at a point P(rθφ) is given as,
     
    Description: 214656.png
  • The electrostatic energy stored in an electric field is given as,
     
    Description: 214646.png
  • For a linear homogeneous material medium, Poisson’s equation for electric potential is given as,
     
    Description: 214637.png
  • If the medium is charge-free (i.e., ρ = 0), Poisson’s equation reduces to Laplace’s equation, given as,
     
    Description: 214629.png
  • For electrostatic boundary value problems, the field Description: 214621.png and the potential V are determined by solving Poisson’s equation or Laplace’s equation.
  • Uniqueness theorem states that any solution of Laplace equation (or Poisson’s equation) which satisfies the same boundary conditions must be the only solution irrespective of the method of solution.
  • A capacitor is a device which stores electric charge and hence electrostatic energy. The capacitance of a capacitor is the ratio of the magnitude of charge on one conductor to the potential difference between the conductors.
     
    Description: 214611.png
     
    The electrostatic energy stored in a capacitor is given as,
     
    Description: 214604.png
  • Method of images is used for solving electrostatic boundary value problems involving an infinite conducting plane.
  • The conditions that an electric field, existing in a region consisting of two different media, must satisfy at the interface between the two media are called electric boundary conditions. These are given as,
     
    For dielectric–dielectric interface:
     
    E1t = E2t, (D1n – D2n) = σ and D1n = D2n (when σ = 0)
     
    For dielectric–conductor interface:
     
    Dt = 0 = Et and Dn = εEn = σ




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