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 Homework Statement
 The figure shows a closed Gaussian surface in the shape of a cube with edge length of 2m. It lies in a region where the nonuniform electric field is given by: E = (3.00x+4.00)i + 6.00j +7.00k N/C, with "x" in meters. What is the net charge contained by the cube?
 Homework Equations
 Flux = E * A = Q(enclosed)/ε0
I'm having a little trouble understanding how to go about solving this problem. I was in class Tuesday and the hint I got from the T.A. running my discussion section was that : "because the electric field is only nonuniform along the x axis, the electric field will both enter(negative flux) and exit(positive flux)the faces along the y and z axis the same, so there will be no net electric flux going through those 4 faces"
Now, taking what he says to be the truth, that would mean to solve this problem, I would simply use : E * A= Q(enclosed)/ε0 , plug in the value for the electric field along the x axis, plug in the value for "x", and solve for Q(enclosed) which would look like: Q(enclosed) = 3.00(2m)+4.00 * A * ε0
However, something I read in my textbook makes me feel like the hint I was given by the T.A. wasn't exactly correct. In my textbook (when talking about electric flux from a uniform electric field through a cube ), it reads:
"The sources of the electric field are outside of the cube. Therefore, if any electric field line enters the volume of the cube, it must also exit somewhere on the surface because there is no charge for the field lines to land on. This means that generally, electric flux through a closed surface is zero if there are no charges (positive or negative) inside the cube."
Now, if this is the case, then what I was told can't be true because the question I am asked to solve is "what is the net CHARGE CONTAINED BY THE CUBE?", meaning that the cube does indeed contain a net charge. So according to my textbook, the net flux through the faces along the y and z axis cant just be zero because there is a charge for those field lines to land on. So now I am just really confused on what to do. Can someone get me in the right direction so I can solve this problem? Thank you!
PS: Here is the diagram I was given for this problem along with the quote I gave from my textbook:
Now, taking what he says to be the truth, that would mean to solve this problem, I would simply use : E * A= Q(enclosed)/ε0 , plug in the value for the electric field along the x axis, plug in the value for "x", and solve for Q(enclosed) which would look like: Q(enclosed) = 3.00(2m)+4.00 * A * ε0
However, something I read in my textbook makes me feel like the hint I was given by the T.A. wasn't exactly correct. In my textbook (when talking about electric flux from a uniform electric field through a cube ), it reads:
"The sources of the electric field are outside of the cube. Therefore, if any electric field line enters the volume of the cube, it must also exit somewhere on the surface because there is no charge for the field lines to land on. This means that generally, electric flux through a closed surface is zero if there are no charges (positive or negative) inside the cube."
Now, if this is the case, then what I was told can't be true because the question I am asked to solve is "what is the net CHARGE CONTAINED BY THE CUBE?", meaning that the cube does indeed contain a net charge. So according to my textbook, the net flux through the faces along the y and z axis cant just be zero because there is a charge for those field lines to land on. So now I am just really confused on what to do. Can someone get me in the right direction so I can solve this problem? Thank you!
PS: Here is the diagram I was given for this problem along with the quote I gave from my textbook:
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