Gauss-Theorem on a solid dielectric sphere

In summary, the conversation discusses the formation of a load system by a point load and load distribution, which creates two regions in space. The conversation also mentions using the Gaussian theorem to find the electric field modulus at a distance r from the center. The calculation of the electric field vector at point P is also discussed, with a discrepancy in the final answer.
  • #1
Guillem_dlc
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Homework Statement
We have an Q=2nC-load uniformly distributed on a solid dielectric sphere of R=1m-radius with center at the coordinate origin of an Oxyz axis system. At the O centre of this sphere there is a negative point charge q=−1nC. Let us consider the points of space P=(0.3,0.4,0)m and S=(1,2,2)m. Calculate:

(a) The electric field vector at points P and Q.

(b) The difference in potential between these points, i.e. V(S)−V(P).
Relevant Equations
Gauss-Law
The load system formed by the point load and the load distribution generates two regions in space corresponding to r<1m and r>1m, i.e. inside and outside the sphere. Given the symmetry of the distribution, by means of the Gaussian theorem we can find the modulus of the field at a distance r from the center.
  • Region r<1m:
    Captura de pantalla de 2020-01-01 01-32-28.png
To find the electric field vector at point P we need the vector that goes from point O to point P, i.e. r→=(0.3,0.4,0), whose module is worth r=0.5. Thus, the field vector is given by:
Captura de pantalla de 2020-01-01 01-32-04.png


Until the last equation I have it well but the result gives me different. The first component is: [−36+9]⋅(0.3)/(0.5) isn't it? Or I don't see it ...
 
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  • #2
Yes, it looks like the final answer has the decimal points in the wrong place.
 
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Related to Gauss-Theorem on a solid dielectric sphere

1. What is Gauss-Theorem on a solid dielectric sphere?

The Gauss-Theorem on a solid dielectric sphere is a mathematical law that relates the electric flux through a closed surface surrounding a charged solid dielectric sphere to the charge enclosed within that surface.

2. How is the Gauss-Theorem on a solid dielectric sphere derived?

The Gauss-Theorem on a solid dielectric sphere is derived from the general Gauss's Law, which states that the electric flux through a closed surface is equal to the net charge enclosed within that surface divided by the permittivity of the medium.

3. What are the assumptions made in Gauss-Theorem on a solid dielectric sphere?

The main assumptions made in Gauss-Theorem on a solid dielectric sphere are that the dielectric sphere is a perfect conductor and the electric field is uniform and radial.

4. What are the applications of Gauss-Theorem on a solid dielectric sphere?

Gauss-Theorem on a solid dielectric sphere has various applications in electrical engineering, such as in the design of capacitors and insulators, as well as in studying the behavior of electric fields in dielectric materials.

5. Can Gauss-Theorem on a solid dielectric sphere be extended to other shapes?

Yes, Gauss-Theorem on a solid dielectric sphere can be extended to other shapes, such as cylinders, cubes, and other geometries, as long as the electric field is uniform and the material is a perfect conductor.

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