Steps to Apply Gauss Law and its Application to Find Electric Field

Gauss law is important in science field and one of the main application of Gauss law is to find electric field through objects.

Here we will first discuss what is Gauss law and what are its application in science and day to day life. We will discuss the various applications of Gauss law and steps to apply Gauss law with the derived examples of an electric field through different objects as well in notes. 

Applications of Gauss law:

Gauss law is used to find out electric field through a Gaussian surface or object and to solve some electrostatics problem. 

To apply Gauss law follow these four steps: 
  1. Define a Gaussian surface. 
  2. Calculate charge "q" (charge inside the surface)
  3. Calculate ø E.ds (Flux linked with a surface)
  4. Put the values in a formula

P.s: If you don't know what is Gaussian surface or how to define a Gauss law then we have whole another article where I have to explain to you what is Gaussian surface and how to define them. To read the article click here. 

For a basic understanding, Gaussian surfaces are such surfaces where angle 'θ' electric field 'E' and area vector 'A' is same at every point on the surface. 

Read this article to understand more clearly where I have explained about this in detail and steps to identify and determine a Gaussian surface.

Daily life application of Gauss law:

Well, there is no use of Gauss law in the daily life of an average human being but Gauss law can be used in acoustic and things related to sound but there is no such practical daily life application of Gauss law.

Steps to apply Gauss law:

So here are the basic steps on how to apply Gauss law to find the electric field from any symmetrical or Gaussian surface.

Step 1: Define a Gaussian surface:

First, you need to define a Gaussian surface. Always remember you don't need to identify a Gaussian body, we need a Gaussian surface so suppose in a cylindrical you don't need to check whether the angle between electric field and area vector is same from all the side or not.

Just decide one surface and check. A body can have more than one Gaussian surface so to avoid confusion name all the surfaces differently and check whether they are Gaussian surfaces or not.

To know more about Gaussian surface and steps to determine a Gaussian surface I have a separate article on it, I will recommend you to read that article in order to understand the Gaussian surface. Click here to read that article.

Step 2: Calculate charge 'q' inside the surface:

Calculate the total charge inside the surface.

Step 3: Calculate flux (E.ds) linked with the Gaussian surface:

Calculate the amount of electric field passing through an area of a Gaussian surface.

Electric flux linked to a surface
Electric flux linked to a surface
The formula for flux is E.ds where 'E' stands for the amount of electric field and 'ds' for surface area. If you want to know about the electric field and electric charge in more detail then we also have a separate article on electric charge and field. Click here to read that article.

Step: 4 Put values of electric charge and flux in a formula:

Put the values of the total number of charge and electric flux in Gauss theorem. Put the calculated value of total electric charge 'q' and electric flux 'E.ds' in formula E.ds = q/ε

Example of Gauss law and applications to find electric charge:

Gauss law is used to calculate the electric charge from a body. Here are some examples and applications of Gauss law that how Gauss law is used to find the electric field through a different object.

1. Electric field due to point charge:

2. Electric field due to linear charge:

3. Electric field due to infinite long plain sheet:

4. Electric field due to charge on conducting shell:

5. Electric field due to sphere of charge:

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