# Electrostatic self energy of a uniform density sphere

• ccheck13
In summary, electrostatic self energy refers to the potential energy of a charged object due to its own electric field. The self energy of a uniform density sphere can be calculated using the formula U = (3/5)(kQ^2)/r and is important in understanding the stability and behavior of charged objects. It follows an inverse relationship with distance, decreasing as the distance between charges increases. The self energy can also be negative in cases where the charges on the sphere have opposite signs, resulting in an attractive force between them.
ccheck13

## Homework Statement

"In class we calculated the electrostatic self energy of a uniform density sphere of charge, i.e., the work required to assemble the sphere from "infinite dispersal." Along the same lines, calculate the electrostatic self energy of a spherical shell of charge, of negligible thickness, radius a, and total charge Q. Note that the radius of the charge distribution does not vary as you build it up.

I think you need to show your work first.

What was your attempt to solution?

## 1. What is electrostatic self energy?

Electrostatic self energy is the potential energy that a charged object possesses due to its own electric field. It is a measure of the work required to assemble or disassemble a system of charges.

## 2. How do you calculate the electrostatic self energy of a uniform density sphere?

The electrostatic self energy of a uniform density sphere can be calculated using the formula: U = (3/5)(kQ^2)/r, where U is the self energy, k is the Coulomb constant, Q is the charge of the sphere, and r is the radius of the sphere.

## 3. What is the significance of the electrostatic self energy of a uniform density sphere?

The electrostatic self energy of a uniform density sphere is important in understanding the stability and behavior of charged objects. It also plays a role in various phenomena, such as the attraction and repulsion between charged particles and the formation of electric fields.

## 4. How does the electrostatic self energy of a uniform density sphere change with distance?

The electrostatic self energy of a uniform density sphere follows an inverse relationship with distance. As the distance between the charges increases, the self energy decreases. This is because the electric field strength decreases with distance, resulting in a weaker interaction between the charges.

## 5. Can the electrostatic self energy of a uniform density sphere be negative?

Yes, the electrostatic self energy of a uniform density sphere can be negative in certain cases. This occurs when the charges on the sphere have opposite signs, resulting in an attractive force between them. In this case, the self energy is negative because work is done by the system as the charges move closer together.

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