Gauss' Law with a cube

[lubuntu]

Homework Statement

Non conducting solid cube with a uniform charge distribution. Why is it impossible, or extremely difficult to calculate the field using a larger cube as the gaussian, what about with a sphere as the gaussian?

Homework Equations

gauss' law

The Attempt at a Solution

I am guessing this is difficult and nearly impossible, at least at our level in both cases because there isn't a very good way of determining what the field would be at some arbitrary point on the Gaussian surface to sum over the entire surface. I am thinking that a sphere wouldn't be very possible either because of the same problem. And the angle of the field compared to the vector dA would be very difficult to determine as well since we really have no idea what the heck the shape of this E field would even look like, as there isn't much symmetry to use?

Am I going in the right direction? I don't think I really understand Gauss' law entirely yet but if I can formulate a descent response to this I think that would certainly improve my understanding.

 

[anathema]

I would like to address your question by first clarifying that Gauss' law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed within that surface. In simpler terms, it helps us calculate the electric field around a charged object.

Now, coming to your question, it is indeed difficult to calculate the electric field using a larger cube as the Gaussian surface for a non-conducting solid cube with uniform charge distribution. This is because, as you correctly pointed out, there is no clear way of determining the field at an arbitrary point on the larger cube's surface. This is because the field is not symmetric around the cube, making it difficult to use any symmetrical approach to calculate it.

Similarly, using a sphere as the Gaussian surface would also be challenging because the electric field around the non-conducting cube is not spherically symmetric. This means that the angle of the field compared to the vector dA would vary at different points on the sphere's surface, making it difficult to calculate the flux through the entire surface.

In conclusion, Gauss' law is a powerful tool in calculating electric fields, but it is limited by the symmetries of the charged object. In the case of a non-conducting solid cube with uniform charge distribution, the lack of symmetry makes it difficult to use a larger cube or a sphere as the Gaussian surface to calculate the electric field. A more general approach, such as numerical methods, would be needed in this case. I hope this helps to improve your understanding of Gauss' law.

 

[tomcue]

I appreciate your attempt at a solution and your curiosity to understand Gauss' law better. You are correct in your thinking that it is difficult to calculate the electric field using a larger cube or a sphere as the Gaussian surface in this scenario. This is because the electric field at a given point is dependent on the charge distribution, and with a non-conducting solid cube, the charge distribution is not easily determined.

In Gauss' law, we use the concept of flux to calculate the electric field. Flux is a measure of the flow of a vector field through a given surface. In this case, the electric flux is the flow of the electric field through a closed surface. By using Gauss' law, we can relate the electric flux to the enclosed charge within the surface. This makes it easier to calculate the electric field since we do not need to know the exact shape or distribution of the charges, but rather just the total charge enclosed within the surface.

However, in the case of a non-conducting solid cube with a uniform charge distribution, there is no clear way to determine the electric flux through a larger cube or a sphere. This is because the electric field is not symmetrical and varies in direction and magnitude throughout the cube. Without symmetry, it is difficult to determine the electric flux and therefore difficult to calculate the electric field using Gauss' law.

In conclusion, it is not impossible to use a larger cube or a sphere as the Gaussian surface in this scenario, but it would be extremely difficult and would require advanced mathematical techniques. It is much easier to use a smaller cube or a sphere, or even a cylindrical or spherical Gaussian surface, as these shapes have symmetries that make it easier to calculate the electric flux and therefore the electric field using Gauss' law.