# 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
*Q*_{1},*Q*_{2}, …,*Q*_{n}placed at points with position vectors respectively then the resultant force on a charge*Q*located at point is,*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
*q*_{1},*q*_{2}, …,*q*_{n}placed at points with position vectors respectively then the electric field intensity is,*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/m
^{2}). It is related to the field intensity 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.
- 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,*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
*Q*_{1},*Q*_{2}, …,*Q*_{n}, located at position vectors respectively then the potential at the point is given as, - 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*(*r*,*θ*, φ) is given as, - Similarly, for an electric dipole with dipole moment and centred at the origin, the field intensity at a point
*P*(*r*,*θ*, φ) 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. *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,
*E*_{1t}=*E*_{2t}, (*D*_{1n}–*D*_{2n}) =*σ*and*D*_{1n}=*D*_{2n}(when*σ*= 0)*D*_{t}= 0 =*E*_{t}and*D*_{n}=*ε**E*_{n}=*σ*