A Gaussian surface in the shape of a cube has edge length 1.14 m. What are (a)[A

Question

A Gaussian surface in the shape of a cube has edge length 1.14 m.

What are (a)[Already solved it] the net flux through the surface and (b)[Already solved it] the net charge (in C) enclosed by the surface if the electric field in the region is in the positive y direction and has a magnitude that is given by E = 4.38y N/C?

What is (c) the net flux if the electric field is in the xy plane and has components Ex = -3.42 N/C and Ey = (5.19 + 3.74y) N/C?

Attempt at Solution:

(1)Relevant equations:

Gauss's Law: e0*net flux = q

Electric flux through a Gaussian surface: Integral (E*dA)

(2) Part A:
Area of the surface, A = (1.14m)^2= 1.2996 m^2;

Thus, the net flux through the surface is (4.38)(1.14)(1.14)^2 = 6.49 Nm^2/C

(3)Part B:
Then the charge, q, is e0*net flux from part A:

(8.85 x 10^-12 C^2/Nm^2)(6.49 Nm^2/C) = 5.74 x 10^-11C

(4)Part C:
Part C: Here's where I ran into problems. Based on an example problem in my text, I reasoned that x-and y-components of E given in part C make up a constant field and thus don't affect the net flux. So, I'd end up with the same result as in Part A, but that's incorrect. I'm not sure how to go about solving the problem at this point.

Explanation / Answer

First, let me say thank you. That is, thank you for doing your own problem and actually having an interest in learning, unlike most people that just post their homework on cramster and wait for someone to give them the answers. I've been answering questions on cramster for almost 5 years now... and in this respect I can accurately say that you're in the extreme minority (top 0.1%?) of cramster users. Anyways. Just had to say that. As for your question... they threw you a little curveball. Look closely at the given field in part c and you will see that the y component is NOT constant (the x component is constant, and you're right... constant E field does not affect the total flux: in one side and out the other). So... basically part c is a lot like part b. You can ignore the constant Ex and the constant part of the Ey (note: 5.19 is constant in Ey; the 3.74y is NOT constant). Just calculate the total flux using the 3.74y, just as you did in part b. Send me a PM if you need to, but I'm betting you have it under control.

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