Gauss Law Problem direction of Area

[Physicslearner500039]

Homework Statement

In Fig. 23-28, a butterfly net is in a uniform electric field of magnitude E = 3.0 mN/C. The rim, a circle of radius a = 11 cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the netting.

Relevant Equations

NA

My attempt is
∅ = ∫E.dA.
The direction of E is going out of the net towards +ve i axis.
I am not clear on the direction of the Area, it can be either +ve i-axis or -ve i-axis. Which direction should i consider?
∅ = ∫3.dA = 3*∫dA ---->1
∫dA is the area of the circle.
A = π * (0.11)^2 = 0.038 m2

Hence
∅ = 3*0.038 = 0.114 NC/m2. Please advise, the answer is negative of this.

 

[etotheipi]

The total flux through the surface consisting of the net and the circular face, taking the area vectors to point out of the surface (i.e. positive flux $\implies$ field lines leaving the surface) $$\Phi = \oint \vec{E} \cdot {d\vec{A}} = \Phi_{net} + \Phi_{circle} = \Phi_{net} + 0.003\pi a^2$$Since $Q=0$, what must be the sign of $\Phi_{net}$? Can you then rationalise this by considering the dot product of the area vectors with the electric field on the netting?