Calculating the Net Charge Enclosed by a Closed Surface

• MissPenguins
In summary, the electric flux through a closed surface is proportional to the enclosed electric charge.
MissPenguins

Homework Statement

A closed surface with dimensions a = b =
0.294 m and c = 0.3528 m is located as in
the figure. The electric field throughout the
region is nonuniform and given by $\vec{}E$ = ($\alpha$+$\beta$
x2)ˆı where x is in meters, $\alpha$ = 2 N/C, and $\beta$
= 4 N/(Cm2).

See figure in the attachment.

What is the magnitude of the net charge
enclosed by the surface?

Homework Equations

I don't know. I am seriously not lazy.

The Attempt at a Solution

Sorry, I don't know. I really have absolute no clue anything about this problem. I don't really understand the concept either. It would be great if you could explain it and help me out. I promised I did try to do it.
THANK YOU!

Attachments

• physicsproblem2.jpg
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Last edited:
Hi MissPenguins!

The relevant equation is Gauss's law: "The electric flux through any closed surface is proportional to the enclosed electric charge".

Perhaps the wikipedia article http://en.wikipedia.org/wiki/Electric_flux summarizes it in a way you can use?

So electric flux = E dot dA?? Can you please explain the concept? Thank you!

Start by calculating the flux across each face of the cube. Do you know how to do that?

vela said:
Start by calculating the flux across each face of the cube. Do you know how to do that?
Is it calculating the area of the cube? Can you please explain the concept? I am watching a youtube video on electric field now. Thanks.

MissPenguins said:
So electric flux = E dot dA?? Can you please explain the concept? Thank you!

E $\bullet$ dA is a vector dot product. You will need to understand what a dot product is in order to calculate the electric flux.

http://en.wikipedia.org/wiki/Dot_product

The flux Φ is a measure of how much electric field is crossing a given area. It's given by
$$\Phi = \int \mathbf{E}\cdot d\mathbf{A}$$
where you integrate over the area in question. In this problem, it's easiest to treat each face of the cube separately.

To make use of the definition, you need to understand what's meant by dA and how to calculate the dot product. I suggest you consult your textbook and notes. You'll get a better explanation in your book than we can provide here (plus it'll probably have helpful pictures you won't get here). If you have any specific questions, post those here.

Alright, thank you very much. My professor will probably explain it tomorrow. Thanks everyone.

1. What is the formula for calculating the net charge enclosed by a closed surface?

The formula for calculating the net charge enclosed by a closed surface is Q = ∮S ρdV, where Q is the total charge enclosed, ∮S is the surface integral, ρ is the charge density, and dV is the volume element.

2. How do you determine the direction of the net charge enclosed by a closed surface?

The direction of the net charge enclosed by a closed surface is determined by the orientation of the surface. If the surface is oriented outward, the net charge will be positive. If the surface is oriented inward, the net charge will be negative.

3. Can the net charge enclosed by a closed surface be negative?

Yes, the net charge enclosed by a closed surface can be negative. This indicates that there is a larger amount of negative charge inside the surface than positive charge.

4. What is the significance of calculating the net charge enclosed by a closed surface?

Calculating the net charge enclosed by a closed surface is important in understanding the behavior of electric fields. It helps in determining the direction and magnitude of the electric field at any point outside the surface.

5. How does the shape of the closed surface affect the calculation of the net charge enclosed?

The shape of the closed surface does not affect the calculation of the net charge enclosed. As long as the surface is completely closed and there are no charges outside of it, the net charge enclosed will remain the same regardless of the shape of the surface.

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