Every matter in this universe is made of atoms. The atoms are electrically neutral. This is because, each atom has the equal number of protons and electrons. Protons have positive charge. In an atom, protons sit in the central nucleus along with electrically neutral neutrons. The protons are strongly bounded in the nucleus. So, protons cannot be detached from the nucleus by any normal process. Each electron revolves round the nucleus in definite orbit in the atom. Electrons have negative charge. The quantity of electric charge of an electron is exactly equal to that of a proton but in opposite in nature. The electrons are negative and protons are positive. So, a piece of matter normally electrically neutral, since it is made of electrically neutral atoms.
The electrons are also bounded in the atoms but not all. Few of the electrons which are farthest from the nucleus may be detached by any means. If some of these detachable electrons of neutral atoms of a body, are removed, there will be a deficit of electrons in the body. After, removal of some of the detachable electrons from the neutral body, the total number of protons in the body becomes more than total number of electrons in the body. As a result the body will become positively charged.
Not only a body can give away electrons, it may also absorb some extra electrons, supplied from outside. In that case, the body becomes negatively charged.
So, deficit or excess of electrons in a body of matter is called electric charge.
Charge of an electron is very small and it is equal to
. So, total 
number of electrons have electric charge of 1 Coulomb. So, if a body deficits 
number of excess electrons, the body will be of 1 coulomb negative electric charge. number of electrons, the body will be of 1 coulomb positive electric charge. On the other hand, if a body has number of excess electrons, the body will be of 1 coulomb negative electric charge.Charged body is an example of static electricity. This is because, the electric charge is confined in the body itself. Here, the charge is not in motion.
But when the electric charge is in motion, it causes electric current. Electric charge has the potential of doing work. That means it has potential to either attract opposite nature of charge or repulse same nature of charge. A charge is the result of separating electrons and protons.
Electric potential at a point in an electric field is defined as the amount of work to be done to bring a unit positive electric charge from infinity to that point.
Similarly, the potential difference between two points is defined as the work required to be done for bringing a unit positive charge from one point to other point.
When a body is charged, it can attract an oppositely charged body and can repulse a similar charged body. That means, the charged body has ability of doing work. That ability of doing work of a charged body is defined as electrical potential of that body.
If two electrically charged bodies are connected by a conductor, the electrons starts flowing from lower potential body to higher potential body, that means current starts flowing from higher potential body to lower potential body depending upon the potential difference of the bodies and resistance of the connecting conductor.
So, electric potential of a body is its charged condition which determines whether it will take from or give up electric charge to other body. Electric potential is graded as electrical level, and difference of two such levels, causes current to flow between them. This level must be measured from a reference zero level. The earth potential is taken as zero level. Electric potential above the earth potential is taken as positive potential and the electric potential below the earth potential is negative. The unit of electric potential is volt. To bring a unit charge from one point to another, if one joule work is done, then the potential difference between the points is said to be one volt. So, we can say,
If one point has electric potential 5 volt, then we can say to bring one coulomb charge from infinity to that point, 5 joule work has to be done. If one point has potential 5 volt and another point has potential 8 volt, then 8 – 5 or 3 joules work to be done to move one coulomb from first point to second.
Potential at a Point due to Point Charge
Let us take a positive charge + Q in the space. Let us imagine a point at a distance x from the said charge + Q. Now we place a unit positive charge at that point. As per Coulomb’s law, the unit positive charge will experience a force,
Now, let us move this unit positive charge, by a small distance dx towards charge Q.
During this movement the work done against the field is,
So, total work to be done for bringing the positive unit charge from infinity to distance x, is given by,
As per definition, this is the electric potential of the point due to charge + Q. So, we can write,
Potential Difference between Two Points
Let us consider two points at distance d1meter and d2 meter from a charge +Q. We can express the electric potential at the point d1 meter away from +Q, as,
We can express the electric potential at the point d2 meter away from +Q, as,
Thus, the potential difference between these two points is
Voltage or Electric Potential Difference
Before understanding voltage or electric potential difference, it’s important to first investigate how a charged particle moves in a uniform static electric field.
Voltage Theory
Let us consider two parallel plates, that are connected to a battery. The upper plate is connected with positive terminal of a battery. Hence this plate is positively charged, and the lower plate is connected to negative terminal of the battery and hence this lower plate is negatively charged.These plates produce a static electric field between them which is proportional to surface charge density of both plates, let’s the surface charge density of the upper plate is σ. Then the surface charge density of lower plate will be – σ. The electric field produced by the only positive plate is surface charge density divided by twice of permeability of the space between the plates
i.e.
Similarly, a static electric field produced by the negative plate is
Hence resultant electric field between the plates is
Let us now assume a positively charged particle enters into that electric field. If the particle has a charge of q Coulomb, then electrostatic force applied on that particle will be
Fe = q.E
Where E is the electric field vector and it is constant for a uniform electric field.
Now acceleration of the particle,
Where m is the mass of the particle. Hence velocity of the particle at any instant t can be written as,
Where Vo is the initial velocity of the particle at the entrance into a uniform electric field.
So, the position of the particle at any instant t can be written as,
Where Po is the initial position of the particle at the entrance into a uniform electric field.
The path is the function of a parabola. Hence it can be predicted from the function that the motion of a charged particle in a uniform electric field is projectile motion in a parabolic path.
Electrical Potential Difference and Definition of Voltage
We can use electric field vector to characterize static electric field in space. By observing the movement of charged particles inside an electric field, one can predict the exact characteristics of that field.
If the field is strong enough, the deflection of a charged particle in a parabolic path will be sharper, and if the field is weak, deflection is less. But it is not the practical way of measuring the intensity of an electric field. Another physical quantity is there which is much easier to measure and also used to characterize an electric field, and this quantity is known as electric potential difference.
The electrical potential V(t) of a position in the electrical field is such that, electric potential energy is required to place a particle of charge q at that position, would be the product of charge of the particle q and the potential of that position V(t). That is potential energy U(t) = q.V(t).The SI unit of electrical potential is Volt, named after an of Italian physicist Alessandro Volta (1745 – 1827). Voltmeters are used to measure the potential difference between two points.
There is a misconception about potential and voltage. Many of us think that both are the same. But voltage is not exactly potential; it is the measure of the electric potential difference between two points.
Electrical Potential and Electrical Field Vector
Electrical potential and electrical field vector, both characterize the same thing that is space of electrical field. Since both electric potential and electrical field vector describe an electric field, they are related.
dV = – E.ds where dV is the potential difference between two points separated by a distance ds and electrical field vector is E.
Definition of Potential Difference or Voltage
After going through the above portion of voltage theory we can now establish a definition of potential difference, definition of voltage in few words. Which says Voltage is the difference in electric potential energy per unit charge between two points.
Voltage is the work to be done, upon an unit charge to move between two points, against a static electric field. A voltage which is a measure of electric potential difference, is the cause of electrical current to flow in a closed circuit.
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