Energy inside a sphere

In summary, the conversation discusses the calculation of electrostatic energy stored in a uniformly charged sphere. The speaker initially solved the problem using the Energy formula, but noticed that online answers and the Griffiths solution manual also included the Electric Field outside the sphere in their calculations. The speaker questions if they were wrong for only considering the Electric Field inside the sphere, but it is clarified that the total electrostatic energy is calculated by integrating the energy density of the Electric Field over all space. This includes the Electric Field outside the sphere, as it reflects the idea that energy is stored in the electromagnetic field rather than the charges themselves. The speaker acknowledges their mistake and understanding is reached.
  • #1
guyvsdcsniper
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37
Homework Statement
The goal of this problem is to find the total electrostatic energy stored in a uniformly charge
sphere of radius R and total charge Q. Note that the charge is uniformly distributed throughout the whole volume –this is not a shell.

Express your answer in terms of Q, R, and constants of nature. There are many different ways to do this, you might want to use two different methods so you can check your result.
Relevant Equations
W= ϵ /2 ∫ E²dt
I solved this problem on my own using the Energy formula. When I compared my answer to online answers (attached) as well as the griffiths solution manual, I noticed they also include the Electric field outside the sphere into their calculations. I did not and only use the Electric Field inside.

Am I wrong for just considering the Electric Field inside the sphere? The problem explicitly states "find the total electrostatic energy stored IN a uniformly charge sphere". I don't see how E outside is relevant to the question.
media_53a_53a1ce99-e699-4af3-ac5b-7ab9ffe09d62_phpaxYpAF.png
 
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  • #2
The energy of a static charge distribution is an integral of the energy density ##(1/2) \epsilon_0 E^2## over all space, which reflects the idea that said energy is stored in the electromagnetic field (which extends over all space) rather than the charges themselves.
 
  • #3
ergospherical said:
The energy of a static charge distribution is an integral of the energy density ##(1/2) \epsilon_0 E^2## over all space, which reflects the idea that said energy is stored in the electromagnetic field (which extends over all space) rather than the charges themselves.
Thank you that makes sense. I actually just got done re reading my book and forgot about the "all space" part of this equation. It makes sense now.
 

1. What is the concept of "energy inside a sphere"?

The concept of "energy inside a sphere" refers to the potential and kinetic energy that exists within a spherical object. This energy can take various forms, such as thermal, electrical, or mechanical, and is determined by factors such as the mass and velocity of the object.

2. How is energy distributed inside a sphere?

The distribution of energy inside a sphere depends on the type of energy present. For example, in a solid sphere, thermal energy is evenly distributed throughout the object, while kinetic energy may be concentrated in certain areas based on the object's motion. In a hollow sphere, the energy is typically concentrated at the surface.

3. Can energy be created or destroyed inside a sphere?

According to the law of conservation of energy, energy cannot be created or destroyed but can only be transformed from one form to another. Therefore, the total energy inside a sphere remains constant, but it can change from potential to kinetic or vice versa.

4. How does the energy inside a sphere affect its behavior?

The energy inside a sphere plays a significant role in determining its behavior. For example, the kinetic energy of a moving sphere can cause it to collide with other objects or bounce off surfaces. The potential energy of a sphere, such as a compressed spring, can cause it to expand or contract when released.

5. What factors influence the amount of energy inside a sphere?

The amount of energy inside a sphere is influenced by its mass, velocity, and the type of energy present. Other factors, such as external forces and the environment, can also affect the energy inside a sphere. Additionally, the material and shape of the sphere can impact the distribution of energy within it.

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