# Finding the energy of a charged sphere

• Eitan Levy
In summary, the conversation discusses the use of a formula for spherical bodies and the potential inside a sphere assuming a potential of 0 at infinity. The integral is done over the volume of the body and the potential inside the sphere is constant and equals KQ/R. However, when trying to do the integral using a constant density and volume element, the resulting value is not correct. The issue is that the potential is not constant inside the sphere if the charge is spread uniformly throughout its volume.
Eitan Levy
Homework Statement
Let's say we have a charged sphere with a radius R and total charge Q with constant density over the sphere. Find the energy of the sphere.
Relevant Equations
V=KQ/R
In class we were taught that for spherical bodies we may use the formula below where the integral is done over the volume of the body. However, if we assume that the potential in infinity is 0, the potential inside the sphere is constant and equals KQ/R, where Q is the total charge of the sphere. If I try to do the integral from r=0 to r=R, while plugging the constant density Q/(4/3*pi*R^3)) and dV=4*pi*r^2*dr, I get a result of KQ^2/(2R). Online I can see it is not right.

What is the problem?

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Delta2
If the charge is spread uniformly throughout the volume of the sphere, then V is not constant inside the sphere.

collinsmark and Delta2

## 1. How do you calculate the energy of a charged sphere?

The energy of a charged sphere can be calculated using the formula E = (1/2)Q^2 / (4πε_0R), where Q is the charge of the sphere, ε_0 is the permittivity of free space, and R is the radius of the sphere.

## 2. What is the significance of finding the energy of a charged sphere?

Finding the energy of a charged sphere is important because it helps us understand the behavior of electric fields and the interactions between charged particles. It also allows us to calculate the potential energy of the sphere and determine its stability.

## 3. Can the energy of a charged sphere be negative?

Yes, the energy of a charged sphere can be negative. This typically occurs when the sphere has a negative charge and is interacting with other charged particles.

## 4. How does the energy of a charged sphere change with distance?

The energy of a charged sphere is inversely proportional to the distance from the center of the sphere. This means that as the distance increases, the energy decreases, and vice versa.

## 5. What is the relationship between the energy of a charged sphere and its electric potential?

The energy of a charged sphere is directly related to its electric potential. The electric potential at a point is equal to the energy per unit charge at that point. Therefore, as the energy of the charged sphere increases, so does its electric potential.

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