Electrostatic Potential
Just as the electric field is described as force per unit charge, electric potential at a point can be described as electrical potential energy per unit charge.
Potential due to a Point Charge
Consider two points 'a' and 'b' in an electrostatic field of a single isolated point charge +q.
Potential due to an Electric Dipole
The potential at point P is the algebraic sum of the potentials due to -q and +q charges.
Potential due to a System of Charges
Potential at a point due to a system of charges is the sum of potentials due to individual charges.
Equipotential Surfaces
Electrostatic field lines help us visualize electric fields. Similarly, potential at various points in an electric field can be represented graphically by equipotential surfaces.
Potential Energy of a System of Charges
Consider two charges q1 and q2 with position vectors r1 and r2 respectively, relative to some origin.
Potential Energy in an External Field
Consider an external electric field 'E' produced by an external source, where it can specified or unspecified. But the potential 'V' due to external source has to be specified.
Electrostatics of Conductor
All materials are broadly classified into two categories, one conductors and other insulators. When a conductor is placed in a electric field, there is a large scale of physical movement of free electrons, within the conductor and they move out only if we make arrangements for it.
Parallel Plate Capacitors
It consists of two conducting plates parallel to each other and separated by a distance 'd', which is small when compared to the length of the plates.
Combination of Capacitors
The potential difference across each capacitor however is different.
Energy Stored in a Capacitor
While charging a capacitor, a battery transfers positive charge from negative to the positive plate. So some work is done in transferring this charge, which is stored in the capacitor in the form of electrostatic energy.
Dielectrics and Polarisation
Dielectrics are non-conducting substances, they have no charge carriers or no free electrons. If an external field is applied, it turns out that charges are induced on the surface which in turn produces a field and opposes the external field. The opposing field does not exactly cancel the external field but only reduces it.
Effect of Dielectric on Capacitance
Capacitance of Parallel Plate with a Dielectric Slab.
Van de Graff Generator
Action of sharp points: Charges are leaked from pointed ends of charged conductors. This creates an electric wind (as moving air is ionized) which moves away from the conductor.
Formulae and Facts
Capacitance of a parallel plate on introducing a dielectric slab (er) of thickness t.
Summary
Potential Energy: is the work done at a point by an external agent in moving a unit positive charge from infinity to a given point against the electrostatic field.
Conclusion
 There has been considerable development in our day to day life due to study and application of Conductors, Insulators, and Capacitors.;
Numerical 01
Calculate the absolute potential at the point P.
Numerical 02
Eight charges having the values shown in figure are arranged symmetrically on a circle of radius 0.4 m in air. Calculate the potential at the centre O.
Numerical 03
If a piece of metal has a charge +0.1mC and is placed inside a hollow metal sphere of radius 20 cm (with touching it), what is the potential of the sphere? What will the potential of the sphere become, if a) the sphere is temporarily Earthed and then left insulated?
Numerical 04
Charges of +20 esu, +9 esu and -5 esu are placed at the corners A, B and C respectively of a DABC shown in the figure. Calculate the potential at the midpoint O of BC.
Numerical 05
Calculate the potential at the centre O of the square.
Numerical 06
Calculate the potential at P due to the charge configuration shown in the figure. If r>>a, then how will you modify the result?
Numerical 07
Calculate the area of the plate of one Farad parallel plate capacitor if the separation between the plates is one millimetre and plates are in vacuum.
Numerical 08
0.5 F capacitor is placed parallel with 0.75 F capacitor and the combination is joined by 110 V DC source. Calculate the charge from the source and charges on each capacitor.
Numerical 09
Assume the radius of electron same to the radius of proton which is 10-15 m. Let the electron charge reside on the surface. What is the potential energy of such as charge distribution? Also, calculate the relativistic mass equivalent of this energy.
Numerical 10
A parallel capacitor of plate area 2m2 and plate separation 5 mm is charged to 10,000 V in free space. Calculate (a) capacitance (b) Charge (c) Charge density (d) Field intensity (e) Field displacement.
