Electric potential due to point charge

In order to find out electrical potential due to point charge, first we consider an isolated point charge 'q' at O. Therefore, the charge produces an electric field around it. We have to find out the electrical potential at a point P at a distance r from the charge. The electric field direction is along OP. Now, let us consider a point A at a distance 'x' from O on the same line OP

Potential difference-its meaning

We have already known potential is the workdone to take the test charge from infinite distance to a point against the electric field.
But potential difference is the workdone by the test charge in taking from one point to another point against the electric field

One point here to remember that the field produced by a positive charge is always directed away from the charge, so we need to do work and hence the potential at any point around the positive charge is positive.

Electrical potential-definition

The electric potential at a point in an electric field is defined as the work done in bringing a unit positive charge from infinity distance to that point against the electric field.
Here we consider that the electric field of the charge and at an infinite distance from it, field strength is zero because the electric potential is more than field strength produced by the charge at infinity.
If an amount of workdone W is done in bringing a test charge q from an infinity to a point against the electric field, then the potential at that point is given by
V=W/q

Electric potential-significance

potentiality means strength, so electric potential means it tells about electric field strength.
Earth is a huge reservoir of charges and hence adding or removing of charges from the earth, there is no change occurs in its potential.
Now let us consider a positively charged body to be connected to the earth by a conducting wire, then it has less number of electrons than usually required. Hence, there is flow of electrons from the earth to the positively charged body. Therefore, conventional current flows from the body to the earth.
Now let us consider a negatively charged body to be connected to the earth by a conducting wire, then it has excessive electrons than usually required. Hence, there is flow of electrons from the body to the earth. Therefore, conventional current flows from the earth to the negatively charged body.
From above two cases, whenever the body gets its required charges, then it becomes neutral charged, i.e., there is no flow of electrons to outside or inside.
So, we say that electrical potential is physical quantity which tells about the field strength i.e., either positive charged or negative charged.

Intensity of electric field due to a point charge

A point charge 'q' is placed stationary at O in air. Place a test charge qo at P. From Coulomb's law, the force experienced by 'qo' is given by

Electric lines of force

To visualize the electric field, Farad introduced the concept of electric lines force. There is a margin between electric field and magnetic field that in magnetic field the lines of force are not end up but in case of electric field that is different i.e., electric lines of force are end up at the poles.

Travelling of passing positive charge along a imaginary curve taken to be the electric line of force. One of the important point to remember that the tangent to the curve at any point will be parallel to the direction of electric field strength at that point.

In a uniform electric field the lines of force are equidistant, parallel and straight lines.

Here are some important points about the electric lines of force as below
1. Electric lines of force always normal to the surface of a conductor.
2. All electric lines of force diverge out from a positive charge and they converge in to a negative charge
3. No two electric lines of force intersect each other. If they intersect at any point, at that point the electric field should have two different directions, which is not possible. The same principle occurs in case of magnetic field
4. Electric lines of force denotes the field strength is strong when lines of force crowded and sparse where the field strength is weak.
5. Electric lines of force are only imaginary lines, but it could not have physical existence.
Some are the important figures tell about the electric lines of force as below

Electric field-intensity of electric field

Electric field is nothing but the space around an electric charge where the electric force due to charge is felt by another charge.
The intensity of electric field or Electric field strength at a point in space is defined as the force experienced by unit positive charge placed at that point.
Suppose we place a test charge q at the point and the force experienced by it is F, then
field strength E=F/q, from it we can obtain the force on the charge F=Eq, here q is test charge taken to be infinitesimally small and positive because we have to take unit positive charge actually, but it is not possible, so that we take like that, unit positive charge is ideal thing.
If the electric field intensity is same in both magnitude and direction at every point of the field, then that electric field is uniform electric field.
If the electric field intensity changes from point to point of the electric field either in magnitude or in direction or in both then that electric field is called non-uniform electric field

resemblance of coulomb's law and gravitational law

Coulomb's law tells about the electrosatic force between two charges, on other hand gravitational law tells about the gravitational force between any two masses.
The electrosatic force is either attractive or repulsive depending on the charges(positive, negative)

From above, the value of K is more and more than the value of G.
From this, we can conclude that the value of electrostatic force is greater than gravitational force. Due to this reason, in nature, even every substance is made up of atoms contains electrons, protons(which causes electricity), electrostatic force does not occur because they uncharged, so that we can gravitational force occurs between them. So, they are fix up to the earth.

Facts about charges

Some are important aspects about the charges as below
1. Like charges are always repel each other and unlike charges attract each other. Even attraction and repulsion takes place even in vacuum also.
2. The force between the charges obeys inverse square law and its magnitude depends on the medium in which charges are placed, the distance between them and also on the magnitude of the charges.
3. The electrostatic force is about 10^35 times stronger than gravitational force, therefore the gravitational force between masses can be usually neglected in comparison with the electrostatic forces.
4. Bodies can be charged by three methods i.e., friction, conduction and induction
5. When a positive charge is brought nearer to an uncharged conductor, then an equal and opposite charge will appear on the conductor on the side nearer, so that the conductor makes the positive charge as neutral nature of the conductor. This process is called induction.
6. Any excess charge given to a conductor, always resides on the outer surface of the conductor.
7. Charges cannot be changed due its motion.
8. The charge density tends to be very large on sharp points on an isolated conductor. Charge density is nothing bout charge per unit surface area.

Electrostatics and its origin

Electrostatics is the branch which deals with forces between the charges which are stationary and about the fields produced by the charges
In 600 B.C., the Greek scholar Thales discovered that when amber is rubbed with fur it attracts small pieces of straw, cork and paper.
Generalisation of this concept is deduced by Dr. William Gilbert stated that many other materials also exhibit the same behaviour as amber.As amber means 'electron', he named this effect as 'electric'
Substances made of atoms. Atom consists of the origin around which electrons move in orbits. Infact, in an atom electrons(negative charge) and protons(positive charge) are equal in number, so that atom is neutrally charged.
But when a glass rod is rubbed with a silk cloth, electrons from glass rod move on to the silk cloth. This transfer of electrons makes glass rod positive (as it looses electrons) and silk cloth negative(as it gets excessive electrons)
Even transfer of electrons from one substance to another substance does not violate the law of conservation of charge because the number of electrons lost by a body is exactly equal to the number of electrons gained by the second body and no new charge is created or destroyed.
The magnitude of the charge on electron is denoted by 'e' and its value is 1.6*10^-19C.
Nobody found that charge is fractional value, therefore charge e=ne(positive or negative), where n is an integer. The quantisation of charge is firstly experimentally proved by R.A.Millikan in his famous Oildrop Experiment.