Parallel Plate capacitor; Formula for capacitance

A parallel plate capacitor is a simple type capacitor in which parallel plates of area A are separated by a distance 'd'. The plates are any shape of square, rectangular or circular. If 'd' is very small compared with the area of 'A', the electric field between the plates will be uniform as shown by equidistant parallel lines of force. However, the field will not uniform at the outer edges of the plates. This shown by curved lines of force in figure. This is called 'fringing' and can be neglected when d<A.

When there is no material in between the plates, air fills the space and acts as dielectric with air as the dielectric, the capacitance of the parallel plate capacitor in terms of plate area(A), distance between the plates 'd' is given by

Principle of superposition

When there are more than two charges, we use this principle of superposition to get the effective force experienced by the a single charge due to presence of all the remaining charges.

According to the principle of superposition, the total effective force exerted on a given charge is the vector sum of all the individual forces that various charges exert seperately on the given charge

Let us consider charges q1,q2,q3..........qn kept stationary at different points. Let the force exerted on q1 by q2 is F12 the force assumed to be independent of other charges(in calculating the F12 we neglect the presence of all other charges excepting q1 and q2)

Similarly let the force exerted on q1 by q3 is F13..........and force on q1 by qn is F1n

Then the total effective force on q1 is given by
F=F12+F13+F14+.......+F1n

The force F12 can be directly calculated by Coulomb's law.

Effect of dielectric on force between charges

Dielectric constants of a medium

Dielectric constant is defined for medium as the ratio of permittivity of the medium to the permittivity of free space

The dielectric constant is also called the relative permittivity of the medium. Where permittivity is physical significance to permit the charge flow in a medium
Dielectric constant will be different for different materials and also it depends upon the temperature and pressure. Dielectric constant for the same material will be different for AC current and DC current. Dielectric constant varies according to the frequency in case of AC current.

Principle of a capacitor

A capacitor is a device to store charges and electrostatic energy. In the simplest form, a capacitor consists of two parallel metal plates separated by a layer of air or a dielectric.
Above figure shows that two parallel plates in which one plate A having positive charge which induces negative charge on other plate B, then the equal amount of positive charge on outside of plate B. The induced charge on the plate B gets neutralized due to earthing. While the induced negative charge on inner side of B is held in position by the attraction of positive charge on A. As this negative charge on B lowers the potential of A.
The principle of a capacitor is to increase the capacitance of a conductor by bringing an uncharged conductor near to it and earthing the outside of the uncharged conductor.
C

Capacitance and its physical significance

Generally, capacity tells about the ability of strength of particular one. When we come to electrostatics in which the capacitance has the meaning but here is what is the quantity denotes about the capacity is that the charge ability of particular device.
Like different containers have difference capacities to fill the liquid, different conductors have the difference capacities to hold the charge. The capacity of a conductor to hold the charge is called
capacitance which is analogous to the volume of container to fill the liquid. Capacitance of a conductor depends on the size, shape and surroundings of the conductor.
In case of isolated conductor, when the charge on the conductor is gradually increases, then its potential will also be increased gradually. Therefore, the charge on the conductor is proportional to the potential.

Relation between the electric field strength and potential difference

From above figure, we have to find out the relation between the electric field strength and the potential difference. There are two points A and B with a distance of 'd' between them.

Electron volt and its significance

Electron volt is the energy acquired by an electron to accelerated through a potential difference of one volt

Magnitude of electron charge e=1.6*10^-19, accelerating potential difference V=1volt
Then the energy acquired by an electron when accelerated through 1 volt P.D. is
W=qV
=1.6*10^-19*1J and is called one electron volt(eV)
To convert the joule to electron volt, one has to divide the value in joul by charge of electron.
The energy levels and ionization energies of atoms and binding energies of molecules are usually expressed in electron volts.
The eV is too small a unit for expressing energies in nuclear physics.

Potential energy of a system of two charges

Let us place positive charge q1 at A, then there is no need to work to place the charge q1 at A because there is no electric field at A. Now, there is electric field around q1. Let us now bring another positive charge q2 from infinity and place it at B at a distance r12 from the charge q1.