What is Electrical Field in a Closed surface with no charge

In summary, a Gaussian Surface has a zero net flux if no charge is enclosed. However, if Electric Field intensity is considered, it is not zero even though the net flux is zero.
  • #1
As per the Gauss Law , Net Flux Electric Field through a closed Surface (Gaussian Surface) is zero if no charge is enclosed.

As per the definition of the Electrical Flux = Electrical Field Intensity dot product Area Vector i.e. Closed Integral of E.S

If Electrical Flux is zero then as per the definition of Electric Flux above , Electric Field intensity through the Gaussian Surface should also be zero, which is not so as shown in the figure below

IMG_20160609_074231~2.jpg


Please clarify why the two results are opposite and which one is correct.
 
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  • #2
Prateek Kumar Jain said:
If Electrical Flux is zero then as per the definition of Electric Flux above , Electric Field intensity through the Gaussian Surface should also be zero,
This is not necessarily correct. A zero net flux could mean that the field is zero everywhere, or it could mean that it points inward on one half and outward on the other half.

Usually you need some more information, like symmetry, in order to make the inference from 0 net flux to 0 field.
 
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  • #3
In your hand writing text you do the mistake in the line ##E\oint dS=0## this is not correct in your example of the sphere inside a uniform field E. The field E is not always perpendicular to the surface element and even when it is, it doesn't have the same direction with the direction of the normal of the surface element.

What happens in your example is that the flux at the left half of the sphere is negative and cancels the flux at the right half which is equal but positive.(remember the positive direction for the normal to the surface element is the one that points outwards from the closed surface.)
 
  • #4
I agree and now I understand my mistake that I was considering Electric Field to be normal to each and every surface element of the Sphere which is not so. Hence Electric Field at the Gaussian surface (Sphere) will not be zero.

Thank you for your explanation Mr. Dale and Delta
 
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1. What is an electrical field in a closed surface with no charge?

An electrical field in a closed surface with no charge is a region in space where an electrically charged particle would experience a force due to the presence of other charged particles. It is represented by electric field lines that show the direction and strength of the electric field.

2. How is an electrical field created in a closed surface with no charge?

An electrical field in a closed surface with no charge can be created by placing a charged particle within the surface. The electric field will then extend outwards from the charged particle in all directions, creating an electric field within the surface.

3. What is the difference between an electrical field in a closed surface with no charge and an electric field in an open space?

An electrical field in a closed surface with no charge is a confined region, while an electric field in an open space has no boundaries. Additionally, an electric field in a closed surface with no charge has a net charge of zero, while an electric field in an open space may have a net charge.

4. How does an electrical field in a closed surface with no charge affect charged particles?

An electrical field in a closed surface with no charge will exert a force on charged particles placed within the surface. The direction and strength of the force will depend on the charge of the particle and the direction and strength of the electric field.

5. Can an electrical field in a closed surface with no charge be manipulated?

Yes, an electrical field in a closed surface with no charge can be manipulated by changing the position or charge of the particles within the surface. Additionally, external electric fields can also be used to alter the electric field within the closed surface.

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