How Do You Calculate the Potential Energy of a Uniformly Charged Sphere?

In summary, the conversation discusses how to calculate the potential energy of a spherical volume of charge using the fact that the electric field outside a spherical distribution of charge is the same as if all the charge were at the center. The result is expressed in terms of the total charge in the sphere. The person asking for help is using a book called Electricity and Magnetism by Purcell to work on this exercise and is grateful for any assistance. The forum rules require showing work before receiving help and a suggestion is given to drop sarcasm to receive more help.
  • #1
ffdbzathf
2
0
A spherical volume of radius, a, is filled with charge of uniform density, p. We want to know the potential energy, U, of this sphere of charge, that is, the work done in assembling it. Calculate it by building the sphere up layer by layer, making use of the fact that the field outside a spherical distribution of charge is the same as if all the charge were at the center. Express the result in terms of the total charge, Q, in the sphere.
 
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  • #2
That was a nice rendition of your exercise question!

Now, going over to the really big issue:
Have you done anything at all?
 
  • #3
Exercise question? This is not for school dude...it's june, school is over. I'm working out of a book called Electricity and Magnetism by Purcell, by myself, and have gotten stuck on this question. Thank you so much for being helpful.
 
  • #4
ffdbzathf said:
Exercise question? This is not for school dude...it's june, school is over. I'm working out of a book called Electricity and Magnetism by Purcell, by myself, and have gotten stuck on this question. Thank you so much for being helpful.

The forum rules require you to show your work (or thoughts/ideas) before you get help.

Also, if you drop the sarcasm, people might be more tempted to help :smile:
 

Related to How Do You Calculate the Potential Energy of a Uniformly Charged Sphere?

What is potential energy?

Potential energy is the energy that an object possesses due to its position or arrangement of particles. It is stored energy and can be converted into other forms of energy, such as kinetic energy.

What are the different types of potential energy?

There are several types of potential energy, including gravitational potential energy, elastic potential energy, and chemical potential energy. Gravitational potential energy is associated with an object's position in a gravitational field, elastic potential energy is related to the deformation of an object, and chemical potential energy is stored in the bonds between atoms in a substance.

How is potential energy calculated?

The formula for calculating potential energy varies depending on the type of potential energy. For gravitational potential energy, the formula is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. For elastic potential energy, the formula is PE = 1/2kx^2, where k is the spring constant and x is the displacement from equilibrium. For chemical potential energy, the formula is PE = nRT, where n is the number of moles of the substance, R is the ideal gas constant, and T is the temperature in Kelvin.

What is the relationship between potential energy and kinetic energy?

Potential energy and kinetic energy are two forms of energy that are interconvertible. Potential energy is converted into kinetic energy when an object moves, and kinetic energy can be converted back into potential energy when the object comes to a stop. The total energy of a system, including both potential and kinetic energy, remains constant.

How does potential energy relate to the conservation of energy?

The concept of potential energy is closely related to the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, the total amount of energy, including potential energy, remains constant. This means that when potential energy is converted into another form of energy, the total energy of the system remains the same.

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