# At least One Faraday Tube Between Every Two Unlike Charges in the Universe

• Narayanan KR
In summary: It will be E(z)=-2z^2+1 and V(z)=-z^2. So the potential at z=2 is not just the result of taking the potential at z=1 and subtracting 1 from it.In summary, Lines of flux are a visualization tool that can be used to represent the electric field. They are integral curves of the field, and infinitely many of them could be drawn in principle. However, counting field lines as if the enclosed charge was the only charge in the universe does not give a correct result.
Narayanan KR

By Classic Coulomb's Law there exists negligible yet non zero force of attraction between two unlike charges in-spite of the distance.
However for electrostatic attraction to work we need at-least one Faraday Tube(Lines of Forces) between the attracting charges, does that means,
1.A single positive charge is connected to all other negative charge in the universe via Line(s) of Forces and vice versa
2. A count of number of flux lines leaving a positive charge will give number of negative charges in the universe, but such will be an Infinite number, then why Gauss's formula gives a finite number of flux lines for a given charge ?
3. With number of flux lines of a charge being constant there will be many possible pairs of unlike charges in the universe that are completely isolated from each other and have exact zero coulumb's force between them.

Delta2 and davenn
"Lines of flux" as drawn in your diagram are a visualisation tool. They are integral curves of the field, and infinitely many of them could be drawn in principle. ##\Phi## is often casually described as the number of field lines passing through a surface, and if you draw a finite number of lines and restrict yourself to surfaces perpendicular to the electric field then it's pretty close to proportional. But it's clearly not actually a literal count of field lines because it's not dimensionless.

Flux through an area is defined as ##\Phi=\int\vec E\cdot d\vec A##. Since ##\vec E## is everywhere defined, you can construct a small area that avoids any lines of flux you have drawn, but still have a non-zero ##\Phi##.

In short, you are over-interpreting a useful visualisation and aid to intuition as a fundamental law. You might be interested in reading my Insight article on the related topic of magnetic field lines.

Last edited:
DaveE, Delta2, Narayanan KR and 2 others
Ibix said:
"Lines of flux" as drawn in your diagram are a visualisation tool. They are integral curves of the field, and infinitely many of them could be drawn in principle. ##\Phi## is often casually described as the number of field lines passing through a surface, and if you draw a finite number of lines and restrict yourself to surfaces perpendicular to the electric field then it's pretty close to proportional. But it's clearly not actually a literal count of field lines because it's not dimensionless.

Flux through an area is defined as ##\Phi=\int\vec E\cdot d\vec A##. Since ##\vec E## is everywhere defined, you can construct a small area that avoids any lines of flux you have drawn, but still have a non-zero ##\Phi##.

In short, you are over-interpreting a useful visualisation and aid to intuition as a fundamental law. You might be interested in reading my Insight article on the related topic of magnetic field lines.

Ibix
Hard to explain where you go wrong in 1-3, in short it is what @Ibix said that you are over-interpreting the field lines tool as a fundamental law. Anyway I 'll try to state my view:

Gauss's law give us the number of field lines from a charge distribution, AS IF that charge distribution was the only one in the universe. That's why it will always give us the same number (as long as we don't change the enclosed charge distribution) regardless of what's happening in the rest of the universe.

So having in mind that, it doesn't mean that because the flux we get from Gauss's law is constant that the coulomb force between some two opposite charges in the universe is zero, and neither 2. will hold because Gauss's law simply doesn't count the field lines as you think it does. Gauss's law counts the field lines as if the enclosed charge was the only charge in the universe (ok i am repeating myself here, sorry).

Narayanan KR
If (on the z axis) you have positive charges at +1 , -1 and negative charges at 2 , -2, then there are no lines of force crossing the z=0 plane.

Narayanan KR
Yes, but the Electric Field E or the potential V at z= -2 (say) will be still a function of both z=1 and z=2

## 1. What is a Faraday tube?

A Faraday tube, also known as a Faraday cage, is a conductive enclosure that blocks external electric fields. It was named after the scientist Michael Faraday, who discovered its properties in the 19th century.

## 2. Why is it important to have at least one Faraday tube between every two unlike charges?

Having at least one Faraday tube between every two unlike charges helps to maintain the balance of electric fields in the universe. This prevents any one charge from becoming too dominant and causing disruptions in the natural order of electric forces.

## 3. How many Faraday tubes are there in the universe?

It is impossible to determine the exact number of Faraday tubes in the universe. However, based on the vast number of charges and electric fields present, it can be assumed that there are an immense number of Faraday tubes spread throughout the universe.

## 4. Can Faraday tubes be created or destroyed?

Faraday tubes cannot be created or destroyed, as they are a natural occurrence in the universe. They can, however, be manipulated or disrupted by external forces, such as strong electric fields or physical damage to the conductive material.

## 5. What happens if there is not at least one Faraday tube between every two unlike charges?

If there is not at least one Faraday tube between every two unlike charges, the electric fields may become imbalanced and lead to disruptions in the natural order of electric forces. This can result in unpredictable and potentially dangerous consequences, such as electrical surges or interference with electronic devices.

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