- #1
scoldham
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Homework Statement
The box-like Gaussian surface of the attached figure encloses a net charge of [tex]+24.0 \epsilon_0 \mu C[/tex] and lies in an electric field given by
[tex]\vec E = [(10.0 + 2.00x) \hat i - 2.00 \hat j + bz\hat k][/tex]N/C
with x and z in meters and b a constant. The bottom face is in the xz plane; the top face is in the horizontal plane passing through y2 = 1.00 m. For x1 = 1.00 m, x2 = 4.00 m, z1 = 1.00 m, and z2 = 3.00 m, what is b?
Homework Equations
[tex]\Phi = \int{E dA}[/tex]
[tex]\int{E dA} = \frac{Q}{\epsilon_0}[/tex]
The Attempt at a Solution
I get that some integration needs to take place over each surface and that the sum of each integration will equal 24 micro coulombs. I can then solve for b. But I'm not sure how the integration needs to happen. What variable do I integrate wrt both x and z? How does that work for the left or right side of the shape? Help very much appreciated!