1. The problem statement, all variables and given/known data I have three questions spanning three different situations, but each deal with the single concept of electric flux. Problem 1: Write an expression for the net electric flux through the entire surface in terms of the area vectors and the electric field E. Problem 2: Consider the left side of the box as consisting of N small pieces. Led dAi represent the area of the ith small surface element on the left side of the box, and let Ei represent the electric field on that surface element. Write an expression for the net electric flux through the left side of the box in terms of dAi and Ei. Problem 3: Suppose that the new charge located to the right of the loop had been negative instead of positive. How would your answer to part b change, if at all? Explain. 2. Relevant equations Φ = ∫E⋅dA Φ = Qenclosed/ε0 3. The attempt at a solution So for the first problem I truly have no idea how to start it. I mean I have to use the vector definition for electric flux to start writing the expressions, but I feel like its just ∫E1⋅dA1 + ∫E2⋅dA2 + ∫E3⋅dA3 since there are three pieces to this one surface. However, I think this is wrong since the integral should be over the whole surface not individual pieces like I have. Thats what dA means correct? For problem 2 its the same issue I am having with problem 1.I don't know if it is looking for what I am doing in problem one with all the subscript 1, 2, 3 scenario or just ∫En⋅dAn. Again confused. For problem 3 I think I have the answer as positive since the electric field is coming toward the negative charge so the positive charge would have its field lines going through the surface as positive lines go away from the charge and then there would be negative field lines going toward the negative charge which come from the positive and elsewhere so the lines would point the same direction as my dA which is to the right as I drew in the first part of the problem. Hopefully that is correct? I know its a lot, but the flux concept is having me confused and the equations are especially daunting.