How Do You Calculate the Electrostatic Energy of a Hollow Conducting Sphere?

• sal1234
In summary, the conversation discusses the relation between work and potential in a charge distribution, and using a specific formula to calculate the electrostatic energy of a hollow conducting sphere with a given charge. The solution involves considering a small spherical element and integrating to find the total energy, but there may be errors in the integration process that need to be corrected.
sal1234
[Note from mentor: this was originally posted in a non-homework forum, so it does not use the homework template.]

There is a general relation between the work U required to assemble a charge distribution ρ and the potential φ(r) of that distribution:
U = 1/2 ∫ ρ φ dv
Now using this specific formula i would like to calculate the electrostatic energy of a Hollow conducting Sphere of Radius ''R'' which is given a Charge ''Q''.

MY ATTEMPT AT THE SOLUTION:

WKT, φ(r) = (1/4πε0)Q/r For every r > R

ρ = Q/R^2

Now let us consider a spherical element of radius "r" and thickness "dr". The potential is uniform in this small element.The energy in this small element is
du = (1/2 )ρ φ dv

dv = area * thickness
dv = 4πr^2 * dr

du = (1/2 ) ρ (1/4πε0) Q/r dr

integerating from R to infinity in order to get the total energy

U = (1/2 ) ρ (1/4πε0) Q/r dr

But i am not able to get right answer.

Last edited by a moderator:

sal1234 said:
integerating from R to infinity in order to get the total energy
Maybe you made something wrong here or later parts. Its hard for me tell, but it can be sometimes hard to take the integral. Try to write the ##dV## in terms of ##dR## and then ##dR## in terms of ##dQ## and then try to take integral. By doing this you ll reduce your calculations a lot. Also make a strict destinction between ##R## and ##r##. And open the ##ρ## When you are taking the integral. It should come out right then..

You need to rethink your integration. The charge density is zero for ##r \ne R##.

vela said:
You need to rethink your integration. The charge density is zero for ##r \ne R##.
what should i do?

You need to carefully define the volume charge density (the surface charge density is as you say, however you need the volume charge density since you going to integrate over a volume) for your problem with the help of a dirac delta function. Then the integral should be easy to calculate.

1. What is electrostatic potential energy?

Electrostatic potential energy is the energy stored in an object due to its position in an electric field. It is a form of potential energy that arises from the interactions between electrically charged particles.

2. How is electrostatic potential energy calculated?

The electrostatic potential energy between two point charges can be calculated using the equation U = kQ1Q2/r, where k is the Coulomb's constant, Q1 and Q2 are the charges of the particles, and r is the distance between them.

3. What factors affect the electrostatic potential energy?

The electrostatic potential energy between two point charges is affected by the magnitude of the charges, the distance between them, and the medium between them. In addition, the presence of other nearby charges can also affect the electrostatic potential energy.

4. What is the relationship between electrostatic potential energy and electric potential?

Electric potential is the amount of potential energy per unit charge at a particular point in an electric field. The relationship between electrostatic potential energy and electric potential is given by the equation V = U/q, where V is the electric potential, U is the electrostatic potential energy, and q is the charge.

5. How is electrostatic potential energy used in everyday life?

Electrostatic potential energy has many practical applications in everyday life, such as in the operation of electronic devices like phones and computers. It is also used in industrial processes, such as electrostatic precipitators for air pollution control. In addition, the concept of electrostatic potential energy is important in understanding the behavior of lightning and other electrical phenomena.

Replies
2
Views
2K
Replies
1
Views
2K
Replies
4
Views
4K
Replies
1
Views
1K
Replies
1
Views
2K
Replies
2
Views
1K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
5
Views
3K
Replies
29
Views
3K