Electric flux, Gauss's Law and electric field

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Introduction


Electric flux refers to the number of electric fields (field lines) that passes through a given surface. If we assume that the surface is completely flat and the electric field is evenly distributed throughout this area, then we can calculate the electric flux by taking the point at which the electric field's product is under a given surface. If the electric field is not constant or the surface is not entirely flat, we need to use the calculation to find the Electric flux.



 In this case, we need to take the integral of the electric field's scalar product and the infinite distance at which the electric field acts. Taking the integral, we essentially divide the region into minimal parts, where the electric field can be considered constant, and the surface can be regarded as flat. Flux is a concept that can be interpreted physically.


 Calculation of the electric field is done by dividing the imaginary surface into smaller surface elements. Each surface element is always seen as a flat surface and is represented by a vector. The size of this vector is the same as the surface element's area, and the direction is perpendicular to the surface. If the surface is closed, then this vector  should leave the closed surface.

Electric Flux


An Electric flux refers to the total number of electric lines of force that goes through any given surface area, held perpendicular to the direction of electric lines of force. It is represented by the Greek letter Ø the surface where electric lines of force cross may either be open or closed. For a closed surface, electric flux is positive (+) if the electric lines of force flow outwards and is negative (-) if the electric lines of force flow inwards and also any surface around the charge +q and negative for surface around charge q₂, the Electric flux is positive.



Electrostatics
Electric flux


Now for an open surface, the electric lines of force of an electric field that is uniform Electric Field (E) are closing a surface of area “A” that is perpendicular to the electric field.  Electric flux Ø, through the surface, is therefore given as
                               


                                           Ø = EA     ...... (i)


Whenever the surface makes an angle θ with the movement or direction of electric lines of force, then the electric flux is given as:


                                               Ø = EA cos θ








Unit :


Of the E and A units, there are Internal System of Units (SI) units of electric current, which is shown below.

 One is Nm² C  ̄¹
The other is JmC  ̄¹
 
The number of force lines that come out of a body that is positively charged decides the body's charge in the coulomb. 


Electric flow units are shown in coulombs. Therefore, if the charge of a positively charged body is q coulomb, then the electric current due to the charged body is Ø = q coulomb.

The electric flux through an area:


The electrical flux through an area is defined as the number of power lines in the area generally passing through that area. This is a scalar quantity indicated by Ø.



flux through an area
Electric flux through an area 



Put an area A in an electric field E, and dA is a vector element of a small area, then we get a small flow (dØ) that passes through a small area (dA);


                               dØ = E.dA ...... (ii)
                                 

                                 
                                  dØ = E dA cos θ ....... (iii)


θ represents the angle between E and dA.
If θ = 0 °, That is,     E || dA, which means the flow is at maximum 
If θ = 90 °, That is,   E ⊥ dA, the flux is zero (0)
Finding the closed surface through the closed surface A, we integrate equation (ii) & (iii) That is,
                    

                         Θ = ∮A  E.Da 
                      

                            =∮ E  dA cos θ


To find the flow through the completely closed surface A, we integrate the equation. (ii) and (iii), That is, 

          

                             
                                        Ø = ∮A E.dA


                                           = ∮A E dA cos θ


Electric flux is a scalar quantity because it is a product of two vector quantities, E and dA.


Electric Field


An electric field refers to a region of space around an electrically charged object or particle where an electric would feel a force. An electric field can be visualized going away or towards charges. If you place a load at any time, the electrical force you feel is proportional to your load. So the force divided by the charge is the same for all the particles at this stage.


This is the electric field at this point. This is vector E: the direction of the electric field coincides with the direction of the force that feels the positive charge at this point. A negative charge will be pushed in the opposite direction of the electric field. 
Electric Field formula:

                                                         F = qE.


F is the electric force


E represents the strength of the electric field.


An electric field created by a positive charge is directed outward along radial lines from its position; for a negative charge, the field indicates its position. It is useful to consider the electric field at each point, indicating the direction. Imagine moving along a curve: at each field, lines start with a positive charge and end with a negative charge. They only cross in places where the electric field direction is not known: where the electric field disappears.


             
Lines of electric field
Electric field


The types of an Electric Field:


There are two types of an Electric field. These are uniform and non-uniform electric fields.


Uniform Electric Field:  It is an electric field where the electric field's direction and intensity remain the same. The electric lines of force remain parallel to each other as well as equidistant.


                  
Uniform electric field
Uniform electric field


Non Uniform Electric Field : It is the field where the intensity of an electric field at different is different. 


                 
Non uniform  electric field
Non uniform electric field



Gauss's law


Gauss's law was named after a German mathematician called Karl Friedrich Gauss. It  states that the Electric flux that passes through any closed surface is proportional to the total load.

 The formula for Gauss's law is;

 Ø = Q/ԑ0

Ø is the electric flux
Q is the enclosed charge
ԑ0  is the permittivity of space
We see this for the simplest case of an electric charge and a sphere. This Gaussian idea holds for all surfaces and any field of electricity. You will find this extremely useful for calculating the electric field of many charge forms.

Applications of Gauss’s law:


Gauss’s law can be used to solve electrostatics problems or find out the electric field through an object

In applying Gauss’s law, these four steps must be followed: 
A Gaussian surface must be defined. 

Charge "q" must be calculated ( that is the charge inside the surface)

 Calculate “ø” E.ds (that is the flux linked with a surface)

Insert the values into the formula

Conclusion:

In conclusion, Electric flux refers to the number of electric field lines passing through a given surface. The article provides some of the main concepts of Electric Flux such as Electric Fields, the types of Electric field, Gauss's law, and the application of Gauss's law. This article provides an understanding of the various concepts of Electric flux .


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