The electric displacement vector field and Gauss' law?

• ppy
In summary, the direction of the electric displacement vector field is always radial for a sphere due to the spherical symmetry of the charge distribution. This can be explained using a Gaussian surface and the symmetry of the system.
ppy
Hi,

I know that for the electric displacement vector field $\oint D.dS$=$\sum Q_{c}$ does this mean that I can just use a Gaussian surface to explain why the displacement vector field for a sphere is radial or not without having to talk about the electric field. If not what is the reasoning to explain that the displacement vector field is radial? or is there just a definition for which direction the displacement field always points in.

Thanks.

There has to be spherical symmetry for the charge distribution. Then symmetry shows that the only direction the D field can have is radial.

1. What is the electric displacement vector field?

The electric displacement vector field is a mathematical concept used to describe the flow of electric flux through a given area. It is denoted by the symbol D and is defined as the electric field strength in a medium, taking into account the presence of any bound charges in the material.

2. How is the electric displacement vector field related to the electric field?

The electric displacement vector field is directly related to the electric field, as it is equal to the electric field plus the electric polarization of the material. In other words, it takes into account the effects of both free and bound charges on the electric field.

3. What is Gauss' law in relation to the electric displacement vector field?

Gauss' law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the total charge enclosed within that surface. In the presence of a dielectric material, Gauss' law is modified to include the electric displacement vector field.

4. How is the electric displacement vector field used in practical applications?

The electric displacement vector field is used in many practical applications, such as in the design of capacitors and other electronic devices. It also plays a crucial role in understanding the behavior of electromagnetic waves in different materials, and is used in the study of optics and electromechanical systems.

5. How is the electric displacement vector field affected by the presence of different materials?

The electric displacement vector field is affected by the presence of different materials, as the electric polarization of a material depends on its composition and structure. Different materials have different dielectric constants, which affect the electric displacement vector field and ultimately the overall electric field in a given system.

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