Application of Gauss' law - some doubts

In summary, the speaker has shared images of applications of Gauss' law, specifically the electric field due to an infinitely long charged wire and an infinite charged plane sheet. The speaker notes that in both cases, the Gaussian surface is a cylinder. In the first case, the electric flux is found for the curved surface on the right side of the cylinder, while in the second case, it is found for both the left and right plane caps. The speaker's doubt is why only one side is considered for the curved surface and both sides for the plane caps.
  • #1
logearav
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Application of Gauss' law -- some doubts

Homework Statement



Revered Members,
I have attached images of applications of Gauss' law namely 1) Electric field due to an infinitely long charged wire and 2) Electric field due to an infinite charged plane sheet.
In both cases Gaussian surface is cylinder.
In the first case, the electric flux is found for curved surface and it has been done for only side that is right side of cylinder in this case
In the second case, the electric flux is found for plane caps but it has been done for both the left plane cap and right plane cap.
My doubt is , why we are doing for only one side for the curved surface and for both sides in the case of plane caps?
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The Attempt at a Solution



 

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  • #2


My fourth attachment.
 

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What is Gauss' law and how is it applied?

Gauss' law is a fundamental law in physics that describes the relationship between electric charges and the electric field. It states that the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space. This law can be applied in various situations, such as calculating the electric field of a point charge or a charged conducting sphere.

How is Gauss' law related to Coulomb's law?

Coulomb's law is an equation that describes the force between two point charges. Gauss' law is a more general formulation of this law, as it is applicable to any distribution of charges, not just point charges. Coulomb's law can be derived from Gauss' law by considering a surface enclosing a single point charge.

Can Gauss' law be used to calculate the electric field inside a conductor?

Yes, Gauss' law can be used to calculate the electric field inside a conductor. This is because the electric field inside a conductor is zero, and Gauss' law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. Since the net charge inside a conductor is always zero, the electric flux through the surface enclosing the conductor must also be zero.

What are some limitations of Gauss' law?

Gauss' law has some limitations, such as only being applicable to static electric fields and not taking into account the effects of magnetic fields. It also assumes a vacuum or a homogeneous dielectric medium, so it may not accurately describe situations with varying permittivity. Additionally, Gauss' law cannot be used for systems with changing electric fields, as it only considers the net charge enclosed at a specific moment in time.

How can Gauss' law be used to determine the electric field of a charged spherical shell?

To determine the electric field of a charged spherical shell using Gauss' law, we can draw a Gaussian surface in the shape of a sphere that encloses the entire charged shell. The electric flux through this surface is equal to the charge enclosed by the surface divided by the permittivity of free space. By knowing the charge and the radius of the shell, we can calculate the electric field at any point inside or outside the shell.

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