Electrical

# Introduction to Electric Field, Definition and Formula

## Electric Field

### Definition:

Introduction to Electric Field, Definition, and Formula- Any region or area, in which electric charges or electric forces operate or act, is called an electric field

or

Electrostatic field. In other words, the region or distance found around any charged body, up to which the attraction force or repulsion force of the body can function, is known as an electric field. Or an empty space around a charge, in which electrostatic force is found, is called an electric field. Any region in which electric charges experience forces is called an electric field or the region in which electric forces act is called an electric field.

If one charge is present at some place then by bringing the second charge closer to the first charge, a repulsion force or attraction force produces between these two charges.  See fig 6.2.

Figure 6.2

This force depends on the magnitude of charges as well as the distance between them. If distance between these two charges is increased gradually, their mutual force will decrease slowly and will reach zero. Thus, both these charges emancipate from effect of one other. A distance found around a charge, till which its attraction or repulsion force acts, is called electric field. If the magnitude of charge is very high, it causes to produce so many stress (the force found in a unit region, is called stress), that center region of the charge becomes useless, after which discharge occurs as a result of generation of an arc or flame.

Stress is represented by hypothetical or imaginary lines of forces. The direction of these lines of forces at any point tends to be from positive charge towards a negative charge. This has been elucidated in figure 6. 3.. That’s these lines emanate from the positive charge and finish up on the negative charge. In other words, the lines of force start from a positive conductor and end up on a similar negative conductor.

Figure 6.3

## Electric Flux

The total number of lines of force emanating from a charge emanating from a charge is called electric flux. An electric field is represented by lines (also sometimes known as tubes) of forces, which are known as electric flux. Like magnetic flux, electric flux is also represented by lines or paths of magnetic flux. Like magnetic flux paths, electric flux paths do not build close loops, they rather emanate from positive electric charges and end up on mutually equal and opposing negative charges. Electric flus is denoted by 𝛹, and it is measured into coulombs.

## Electric Lines of Force

Electric lines of force are such a path, on which a very minute positive charge moves in an electric field. As a magnetic effect is represented by surrounding magnetic lines of force, likewise electrostatic lines of force exist around an electric charge in electrostatics. These lines emanate from positive charge and end up on to a negative charge. The difference between magnetic lines of forces and electric lines of forces is that electric lines of force do not form a close circuit at all. Under MKS system, a line of force is supposed to be emanated from a unit charge or 𝓆 lines of force emanating from 𝓆 units charge, irrespective of whatever the type of the surrounding insulating media. These lines of force, uniformly emit from charge through all directions, as has been illustrated in figure 6.4.

Figure 6.4 – Lines of forces of a charge

Figure 6.5 – Lines of forces are normal to surface

If a positive charge is put close to a charge of + 𝓆 units and it is free for motion, then lines of force also indicate the path, on which positive charge will move. The arrow signs will reflect the direction of movement of such a charge.

### Properties of Lines of Forces

Electric or electrostatic lines of forces have the following properties;

1. They emanate from a positive charge and close on a negative charge.
2. It always remains normal to the body’s surface at the point, from where they emanate or end up. In other words, two lines never pass through a single point, as has been shown in figure 6.5.
3. When a unit positive charge is placed near a positively charged body, it will adopt the path of lines of force, and will move towards the negatively charged body.
4. A line of force is such that making a tangent on one of its points, it indicates the direction of electric intensity on that point.
5. The lines of force shrink longitudinally, which indicate a status of electrostatic attraction. That’s two opponent charges attract towards each other as a result of shrinking of the lines of force in its longitudinal direction. This has been illustrated in figure 6.2.
6. The lines of force scatter in a perpendicular direction, which indicates a condition of electrostatic repulsion. It means that two similar charges repel each other as a result of spreading of lines of force in an inverse direction. This has been shown in figure 6.2.
7. The lines of force do not exist inside the conductor at all.

## Electrostatic Induction

It has been revealed through experiments that when a uncharged body is brought nearer to a charged body, it also gets charged. This condition of charging an uncharged body merely by bringing it nearer to a charged body, is called electrostatic induction. The phenomenon of an uncharged body getting charged merely by the nearness of a charged body is known as electrostatic induction.

Fig. 6.7

In figure 6.7, a positively charged body A is brought nearer to a fully insulated uncharged body B. It has become known by doing so that a negative charge builds up on that end of B which is nearer to A, whereas, a positive charge creates on the remote end of B. The negative and positive charges of the body B are called induced charges. B’s negative charge is known as bound charge, because it exists on B until A’s positive charge exerts on it. However, the positive charge found on the remote end of B as compared to A, is called free charge. If body B is earthed, then positive charge flows towards the earth, as has been shown in figure 6.7. As such, merely a negative charge is left on body B. After this, even if body A is removed, even then this negative charge will pass on to the earth, and body B will get uncharged once again. The following outcomes can be inferred from the above discussion.

(i). A negative charge generates from a positive charge, and conversely a positive charge creates from a negative charge.

(ii). Every induced charge is equal to its inducing charge.

## Electric Field Strength or Field Intensity or Electric Intensity

The electric field strength (or electric field intensity or electric force) can be defined in the following ways;

(i).  The mechanical force on a point charge of one coulomb at any point in an electric field, is called the electric force or electric field strength.

(ii). If a positive unit charge is placed on some point in an electric field, then force which will affect this charge, is called electric field intensity, and the direction towards which positive unit charge moves, denotes the direction of the field. It is represented by E and its unit is Newton / Coulomb.

For example, if a Q coulomb charge is placed at a certain point P in an electric field, an F Newton force exerts on it. As such, the value of electric field at this point will be as follows;

E = F / Q Newton / Coulomb

The value of E generated as a result of one point charge in the field can also be determined through coulomb’s law;

(iii). Electric intensity at a point may be defined as equal to the lines of force passing normally through a unit cross – section at that point. Let us assume that the magnitude of charge is Q coulombs, and the number of lines of forces generated through it, is Q / Ԑ. If these lines exist around this point in an area of A square meter, then electric intensity found on this point will be as follows;

E = Q / Ԑ /A       = Q / Ԑ A

As D = Q / A, i.e., flux density (D) equals to the charge per unit area, therefore;

E = D / Ԑ = D / Ԑ0 Ԑr … (in a medium)

Or E = D / Ԑ0 … (in air)

In this situation, unit of E tends to be volt / meter.

(iv). The value of electric intensity at any point of electric field equals to the potential gradient at that point. In other words, the value of E equals to the rate of decrease of potential in the direction of lines of force. That’s;

E = -dv/ dx

Electric intensity at any point in an electric field is equal to the potential gradient at that point or E s equal to the rate of fall of potential in the direction of the lines of force. In this situation too, the unit of E is volt/meter. Remember, that potential gradient (dv / dt) is per meter potential drop in the direction of electric field.

## Electric Flux Density or Electric Displacement

The normal flux value existing in a unit area, is called electric flux density. It is denoted by D. it is given by the normal flux per unit area. If flux ψ pass through a square meter area A, then the value of flux density will be as follows;

D = ψ / A C/m2

The following relation is found between electric field density and flux density;

D = Ԑ0 Ԑr E … (in a medium)

D = Ԑ0 E … (in free space)

In other words, the product of electric intensity E and absolute permittivity Ԑ (because Ԑ = Ԑ0 Ԑr) at any point on of a dielectric medium, is known as electric flux density of that point. It must be remembered that electric flux density is also known as electric displacement (D).

Comparison Between Electrostatic and Electromagnet Terms

 Electrostatics Electromagnetism Term Symbol Term Symbol Electric flux Electric flux density Electric field strength Electromotive force Electric potential difference Permittivity of free space Relative permittivity Absolute permittivity = electric flux density / electric field strength i.e., Ԑ0 Ԑr = Ԑ = D / E Ψ D E E V Ԑ0 Ԑr Magnetic flux Magnetic flux density Magnetic field strength Magnetomotive force Magnetic potential difference Permeability of free space Relative permeability Absolute permeability = magnetic flux density / magnetic field strength i.e., μ0 μr = μ = B / H Փ B H F μ 0 μr

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