# Electric energy of a dielectric sphere

• hhh79bigo
In summary: ZguBIn summary, the electric energy of a dielectric sphere is proportional to the surface charge density and inversely proportional to the sphere's radius.
hhh79bigo
Electric energy of a dielectric sphere!

Hi there, I have attempted a question, I was just seeing if some one can go over it and check if it is ok!

Q. The Electric field E inside a dielectric sphere placed between the plates of a large parallel-plate capacitor is uniform. Given that the sphere has a relative dielectric constant "epsilon(r)" and radius r, find an expression for the total electric energy of the sphere.

My working out is as attached to this message:

If there is more that can be done then can you help aswell!

Thanks alot

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It looks like you've answered the question as if the charge on the plates is known. I would have presumed, from the wording of the question, that the Electric Field is known. This would make the Electric field energy within the sphere obvious (epsilon E^2 Volume), but the total Electric (potential) Energy *of* the sphere would not be trivial to calculate. In my view, the surface charges are what actually belong to the sphere; the external E-field belongs more to the environment than to the sphere.
I would've found the surface charge density first, then the Electric PE due to that surface charge density by surface integration. That way you end up *showing* the utility of the new Energy density approach (which I suppose is the "new topic").
of course, I've been known to misinterpret questions before ... .

I don't fully understand, do i have to use maxwells equations to find the charge density, and if so how does this apply to a dielectric between 2 capacitor plates. I thought that the E field would be E(0)/EPSILON(r) where E(0) is the Electric field of the capacitors without the dielectric.

using DIV(E)=Charge desnsity/epsilon(0) I think I'm right in saying this is one of maxwells equations.

Hope you can help clarify this for me. Thanks a lot for you help

hhh79bigo

## 1. What is electric energy of a dielectric sphere?

The electric energy of a dielectric sphere refers to the amount of energy stored in the electric field within the sphere due to the presence of a dielectric material. It is a measure of the potential energy that can be released when the electric field is disrupted.

## 2. How is the electric energy of a dielectric sphere calculated?

The electric energy of a dielectric sphere can be calculated using the formula U = (1/2) * (ε - 1) * V^2, where U is the electric energy, ε is the permittivity of the dielectric material, and V is the potential difference between the inner and outer surfaces of the sphere.

## 3. What factors affect the electric energy of a dielectric sphere?

The electric energy of a dielectric sphere is affected by the permittivity of the material, the size and shape of the sphere, and the potential difference between its inner and outer surfaces. It is also influenced by the presence of any external electric fields.

## 4. How does the presence of a dielectric material affect the electric energy of a sphere?

The presence of a dielectric material in a sphere increases its electric energy due to the polarization of the material, which results in the formation of an electric field within the sphere. This leads to an increase in the potential energy stored within the sphere.

## 5. How is the electric energy of a dielectric sphere used in practical applications?

The electric energy of a dielectric sphere is used in various practical applications, such as in capacitors, where it is stored and released in a controlled manner. It is also utilized in the design of electrical insulation materials and in the development of energy storage devices.

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