# 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,

• If there are a number of charges Q1, Q2, …, Qn placed at points with position vectors  respectively then the resultant force on a charge Q located at point is,

This is known as principle of superposition of charges.
• The electric field intensity  is defined as the force per unit charge when placed in an electric field. So, for a point charge, the field intensity is,
•
• If there are a number of charges q1, q2, …, qn placed at points with position vectors respectively then the electric field intensity is,

This is known as principle of superposition of field.
• The electric field intensity due to different continuous charge distribution is given as,

• The electric flux density  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,

Hence, electric flux through a surface is given as,

• 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 .
• 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 .
• 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,

, integral form

, 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,

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,

• If there is a number of point charges Q1, Q2, …, Qn, located at position vectors  respectively then the potential at the point  is given as,

This is known as principle of superposition of potential.
• The electric potential due to different continuous charge distribution is given as,

• 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,

• 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  and centred at a position vector , the potential at a point P(rθφ) is given as,

• Similarly, for an electric dipole with dipole moment  and centred at the origin, the field intensity at a point P(rθφ) is given as,

• The electrostatic energy stored in an electric field is given as,

• For a linear homogeneous material medium, Poisson’s equation for electric potential is given as,

• If the medium is charge-free (i.e., ρ = 0), Poisson’s equation reduces to Laplace’s equation, given as,

• For electrostatic boundary value problems, the field  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.

The electrostatic energy stored in a capacitor is given as,

• 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