Proving electric lines of forces can't be discontionous in charge free

In summary, the conversation discusses the concept of electrostatic field lines and why they cannot be discontinuous in a charge-free region. One person proposes a unique proof involving Gauss' law, but another person points out that the property of field lines is more of a definition rather than something that needs to be proven. The conversation ends with a question about the consequences of a small test charge traveling along a field line.
  • #1
namanjain
70
0
Hey guys
i had a question in my paper
why electrostatic field lines cannot be discontinuous in charge free region

i guessed a weird (but an innovative proof)
Tell me is it correct

So here it goes
"Let's assume that ELOF can be discontinuous

Then i draw a diagram of broken electric field
Now at one of the two free ends i assumed a small Gaussian volume(Only the free end)
Now using gauss law
ø:FLUX
ø = ∑Qenclosed/ε
ELOF ARE ENTERING BUT NOT ESCAPING SO ø≠0
BUT ∑qENCLOSED=0
SO OUR ASSUMPTION IS FALSE
H.P."
 
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  • #2
Gauss' law sort-of assumes that field lines cannot be discontinuous: so, by invoking it like that you are assuming the statement you are supposed to be proving.
Note: you don't need more than one free end in the hypothetical diagram.

The property is more part of the definition of "field line" so it is not something you prove exactly.
I suppose you could look at the consequences in terms of a small test charge... it travels along a field line to the end, then what?

You describe the Gauss' law argument as "novel" - have you been provided with a different "proof"?
 

1. What are electric lines of force?

Electric lines of force, also known as electric field lines, are imaginary lines used to represent the direction and strength of an electric field. They show the path that a positive test charge would take in the presence of an electric field.

2. Why is it important to prove that electric lines of force can't be discontinuous in charge-free space?

It is important to prove this because it is a fundamental property of electric fields. If electric lines of force were discontinuous, it would imply that the electric field itself is discontinuous, which goes against the laws of physics.

3. How can we prove that electric lines of force can't be discontinuous?

This can be proven using the Gauss's law for electric fields. According to this law, the electric flux through any closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. If electric lines of force were discontinuous, the electric flux through the surface would not be constant, leading to a violation of this law.

4. Are there any real-life examples that demonstrate the continuity of electric lines of force?

Yes, there are many examples. For instance, the electric field of a point charge is continuous in all directions. Similarly, the electric field between two parallel plates is also continuous and uniform. These examples show that electric lines of force cannot be discontinuous in charge-free space.

5. Can electric lines of force be discontinuous in the presence of charges?

No, electric lines of force cannot be discontinuous even in the presence of charges. This is because charges create electric fields, and the electric field itself must be continuous. Any discontinuity in electric lines of force would imply a discontinuity in the electric field, which is not possible.

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