# Net charge contained by a cube in a region with a non-uniform E field

• mhrob24
In summary: And that is what you might expect, because the configuration is not symmetric in the x-direction.But aren't the faces along the y and z axis parallel to the x-axis? And if they are parallel, then shouldn't their fluxes cancel?No, the faces along the y and z axis are perpendicular to the x-axis. And as I mentioned before, the fluxes through the faces parallel to the x-axis do cancel. It's the fluxes through the faces normal to the x-axis that don't cancel.Oh, I see! So the fluxes through the faces parallel to the x-axis cancel because the field is uniform along those faces. But the fluxes through the faces perpendicular to the x-axis don't cancel because the
mhrob24
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 non-uniform 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?
Relevant 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 non-uniform 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 can't 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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mhrob24 said:
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 ),
This is talking about a uniform field. Your field is not uniform.

Edit: So, put logically, your textbook is saying field line in means field line out because there are no charges to "land on". This does not mean that charges to "land on" means that a particular field line must "land on" a charge, just that some field lines do.

I'm still confused for 2 reasons:

1. the field along the y and z axis in my problem IS uniform (from what I was told by my T.A.) because it doesn't depend on where you are along the y or z axis; whereas the field along the x-axis is not uniform because it depends on the distance "x".

2. From what you're saying, that would mean that not all electric field lines will land on the charge inside the cube, only some will. If that is the case, then what I was told was indeed incorrect because that means that the flux going through the faces along the y and z axis won't just cancel out because SOME of the field lines will land on the net charge, thus the field won't exit and enter with the same value. I was told by my T.A. the flux going in and out of these faces will cancel...

mhrob24 said:
Q(enclosed) = 3.00(2m)+4.00 * A * ε0
That's the flux out through one end. You need to subtract what came in at the other.
mhrob24 said:
From what you're saying, that would mean that not all electric field lines will land on the charge inside the cube, only some will.
Yes, but that does not mean the fluxes through the faces parallel to the x-axis do not cancel. It can just mean that the fluxes through the faces normal to the x-axis do not cancel.

## 1. What is net charge contained by a cube?

The net charge contained by a cube is the total amount of electric charge that is located within the boundaries of the cube. This charge can be either positive or negative, depending on the types and amounts of charges present within the cube.

## 2. What does it mean for an electric field to be non-uniform?

A non-uniform electric field is one in which the strength or direction of the field varies at different points in space. This can be caused by the presence of different charges or materials in the surrounding area, resulting in an uneven distribution of electric field lines.

## 3. How is net charge contained by a cube affected by a non-uniform electric field?

In a non-uniform electric field, the net charge contained by a cube can be affected in several ways. If the electric field is stronger in one region of the cube than another, the charges within the cube may redistribute themselves, resulting in a change in the net charge. Additionally, if the electric field is changing over time, the net charge may also change due to the movement of charges within the cube.

## 4. Can net charge contained by a cube be zero in a non-uniform electric field?

Yes, it is possible for the net charge contained by a cube to be zero in a non-uniform electric field. This can occur if the positive and negative charges within the cube are distributed in such a way that they cancel each other out, resulting in a net charge of zero.

## 5. How is the net charge contained by a cube calculated in a non-uniform electric field?

The net charge contained by a cube in a non-uniform electric field can be calculated by summing up the individual charges within the cube and taking into account the direction and strength of the electric field at each point within the cube. This can be a complex calculation and may require advanced mathematical techniques, such as Gauss's law.

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