How Well Do You Understand Gauss's Law?

[roflcopter]

Consider Gauss's law: <br /> \oint \vec{E}\cdot d\vec{a} =\frac{Q_{enc}}{\epsilon_0} . Which of the following is true?

A. E Must be the electric field due to the enclosed charge

B. If q=0 then E=0 everywhere on the Gaussian surface

C. If the charge inside consists of an electric dipole, then the integral is zero

D. E is everywhere parallel to dA along the surface

E. If a charge is placed outside the surface, then it cannot affect E on the surface.
The attempt at a solution

I've ruled out B: Because I can have a point charge outside the Gaussian surface and so E is not zero necessarily at the surface since it will create an E field.

I've ruled out D: Because I can have a cube and E will not always be parallel to the 6 sides. Only case I can think of E being always parallel to dA is for a sphere.

I've ruled out E: Because this is similar to B. The external charge will create an E field of E=kQ/r^2.

So I say the answer is C since q(enclosed) will be zero leaving the integral equal to zero. Or, the answer could be A since isn't that kind of the definition of Gauss's law anyways? Or well, I guess not since we could have a Gaussian surface with no charge in it and a charge outside with E=kQ/r^2. So, the E vector in the integral is not necessarily due to the charge inside the Gaussian surface, right?

I don't think I'm supposed to have multiple answers though...not sure. I'm leaning more towards answer C.

 

[Delphi51]

I don't like A. E is the electric field due to all charges in the universe, not just the ones inside. As you said in your comment on B.