If there were only one charge in the universe.

the-ever-kid

there was this question that i saw in a book and it also had an answer .

(this is not a homework question)

The Question was:

• [itex]\phi = \oint_s\boldsymbol{E}.\partial\boldsymbol{ A}\neq 0[/itex] on any surface
• [itex]\phi = \oint_s\boldsymbol{E}.\partial\boldsymbol{ A}=0 [/itex] if the charge is outside a surface
• [itex]\phi = \oint_s\boldsymbol{E}.\partial\boldsymbol{ A} [/itex] is not defined
• [itex]\phi = \oint_s\boldsymbol{E}.\partial\boldsymbol{ A}=\frac{q}{\epsilon_o} [/itex] if the charge is outside a surface

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.

mfb

Why? What would be wrong with a universe with only electrons inside?

If you plan to remove the option to have opposite charges from the whole theory, you might have to reformulate quantum electrodynamics. But that is not part of the question here, I think.