Would electric field exist if there were only one type of charge?

[navneet9431]

Homework Statement

If there were only one type of charge in the universe, then:

ϕ=∮E⋅∂A≠0 on any surface.
ϕ=∮E⋅∂A=0 is the charge is outside a surface.
ϕ=∮E⋅∂A will not be defined.
ϕ=∮E⋅∂A=qϵo if the charge is inside the surface.

Relevant Equations

Gauss Law
Φ=∫E⋅dA

The answers were given as being the second and the last option.

I believe the answer is incorrect, reasons:

1. The answer assumes that electric field will exist .
2. But this is not the case , until and unless there is a bipolarity there cannot be an electric field ( in case of isolated charged objects, the field exists because the bipolarity is separated by a distance ∞ )
3. This integral will result in a constant 0 as the electric field will be zero.(all cases)

I want to know if my reasons are correct or not if not then why is the given answer correct or wrong and what should be the correct answer?

 

[Orodruin]

Your reasons are not correct. The given answers are correct if you change the last one to "inside" instead of "outside" (otherwise the second and the last are obviously in disagreement).

The existence of the electric field has nothing to do with the actual existence of charges or particular types of charges.

 

[navneet9431]

Your reasons are not correct. The given answers are correct if you change the last one to "inside" instead of "outside" (otherwise the second and the last are obviously in disagreement).

The existence of the electric field has nothing to do with the actual existence of charges or particular types of charges.

So is it correct to assume this world made up of only one type of charges(electrons)?
Would the assumption that only one type of charges exist not affect Gauss Law?

 

[Orodruin]

So is it correct to assume this world made up of only one type of charges(electrons)?
Would the assumption that only one type of charges exist not affect Gauss Law?

It depends on what you mean by "correct". It is not compatible with what we actually observe from Nature. However, there is absolutely nothing wrong with theoretically considering such a situation.

No, not at all.

 

[navneet9431]

if you change the last one to "inside" instead of "outside"

Thanks for your explanation!
But,What is meant by this line?

 

[Orodruin]

Your original post read (at least on my screen)

ϕ=∮E⋅∂A=qϵo if the charge is outside the surface.

It should be "inside" as it is now.

 

[kuruman]

Just a remark. If there were only one kind of charge in the Universe, would the Universe not necessarily have a net charge? If this charge is localized, then the question can be answered by considering a Gaussian surface that encloses all, some or none of the charge. If the charge is (perhaps uniformly) distributed over the entire Universe, see
https://www.physicsforums.com/threads/breakdown-of-gauss-law.926835/

 

[Orodruin]

Just a remark. If there were only one kind of charge in the Universe, would the Universe not necessarily have a net charge? If this charge is localized, then the question can be answered by considering a Gaussian surface that encloses all, some or none of the charge. If the charge is (perhaps uniformly) distributed over the entire Universe, see
https://www.physicsforums.com/threads/breakdown-of-gauss-law.926835/

Yes, but we are clearly not describing our actual universe here. I do not see a self-contradiction in having a total net charge in Maxwell’s electromagnetism.