Find field due to the infinitely long straight wire

You can’t deny the fact that electromagnetism and physics still haunts you in dreams. Well, don’t worry, almost everyone is scared of this topic. You will learn about one of the famous laws of electromagnetism, i.e. Gauss law. It helps to connect the electric field and charge of a given body.

It’s also a part of the four laws of Maxwell. Let’s understand in detail and learn how to find a field due to the infinitely long straight wire and its effects. 

What is electric flux?

Consider an object and pass a torchlight through it. You will find some rays are directly crossing it while others are not. In the same way, electric flux refers to the number of electric field lines crossing a closed surface perpendicularly.

In physics, this helps to establish a relationship between the electric field and the charge enclosed in a closed object.

To turn on to our next topic, it’s important to learn this topic in-depth, as it forms the basis of Gauss law. With the help of electric flux, you can calculate the field due to infinitely long straight wire. 

Mathematical expression for electric flux

The number of field lines crossing a given area in unit time is known as electric flux. The electric flux depends upon the orientation of the surface. 

Case 1:

So according to the situation, if the surface is directly perpendicular to field lines crossing it.

Then, the flux is,

              =E*A

Case 2:

But, if the surface is bent at some or other angle, then the flux is,

               =E*Acos  

Where, 

is the electric flux

E is the electric field 

A is the area of the surface

  is the angle between the surface and the direction of field lines crossing it. 

What is Gauss Law?

This law plays a vital role if you are a student of physics. This law came into use by the famous scientist Gauss, who stated that the flux due to closed objects is equal to the charge enclosed in a cylinder divided by the permittivity of vacuum. Once you reach the end of this article, you will understand this topic clearly and will be able to create a mind map connecting all the parts of this topic. You are surely going to enjoy this process. 

Mathematical Expression for Gauss Law

As per the Gauss Law, the total flux in a closed surface is charged enclosed by the object, divided by the permittivity of its medium. 

So,  

=E.ds= Eds

ds= 4r2

= E*4r2

The charge inside the Gaussian surface is q

So, according to the Gauss theorem,

=q/

On equating both flux

We get, 

E*4r2=q/

Where, 

E is the electric field of the closed surface

R is the radius of the surface

Q is the charge enclosed by the surface

is the permittivity of the medium 

Let’s take an example a charge is there at a side of a cube, then the flux through each face will be

=Q/

If you take a look at this law closely, you will observe that the total flux by the closed surface is proportional to the charge enclosed by the closed surface. 

How to apply Gauss Law?

This law is the key to calculating the electric field for any type of fixed closed surfaces like a cylinder, cube and many more. If you are facing difficulties while calculating the electric field for any closed surface, then Gauss law will be there to help you.

Steps to Apply Gauss Law

The steps to apply Gauss law at any closed complicated figures are as follows. 

• First, you need to select a Gaussian surface. You would be able to derive the electric field easily. 
• Recollect the symmetry problems of standards 1 and 2. Apply those concepts here for a quick answer. 
• Point to be noted is that it’s not necessary for a Gaussian surface to cover the whole real surface. This could include either the inside or outside of the Gaussian surface. 

Applications of Gauss Law

Gauss law is a very useful law when you need to calculate the electric field of a closed surface.

• Electric field due to infinitely long wire
• Electric field due to a closed sphere
• Electric field due to infinite plane sheet
• Electric field due to a finite wire 

Field due to infinitely long straight wire

Consider a charged infinitely long straight wire. Lambda is the charge per unit length of this object. The straight wire resembles a cylinder if we draw a Gaussian surface around it.

Let the height of this cylinder be l and the radius of its surface be r.

The electric field due to infinitely long straight wire is E.

The total surface area of the curved part= 2rl

Total charge =  l

Flux through the curved surface= E*2rl

According to Gauss law:

E = 2r

Conclusion

With this article, you will gain an understanding of electric flux, Gauss lawand the field due to infinitely long straight wire. To understand these concepts perfectly, you need to practice these topics on a regular basis. With daily practice and learning, you will be a pro at these topics.