# Energy of Coaxial Cylindrical Shells

• NeedPhysHelp8
In summary, The problem involves calculating the energy per unit length for two long coaxial cylindrical shells with radii a and b and linear charge densities λ and -λ, respectively. The electric field in various regions is found using Gauss' Law, and the formula for energy per unit length is given as E=1/2 \int \lambda V \ dl. The question of how to find the potential V(r) is raised, and it is suggested to find V(r) by integrating the electric field over a distance.
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## Homework Statement

Calculate the energy per unit length for two long coaxial cylindrical shells, neglecting end effects. The inner and outer cylinders have radii a and b, and linear charge densities λ and -λ, uniformly distributed on the surface, respectively.

2. The attempt at a solution

Alright so first thing I did was calculate the electric field in various regions using Gauss' Law:
i) for r<a E=0
ii) for a<r<b $$E=\frac{\lambda}{2\pi \epsilon r}$$
iii) for r>b E=0

Now I'm not too sure how to find the energy per unit length: we have the formula $$E=1/2 \int \lambda V \ dl$$ so should I just find the potential V(r) then sub it into that equation?
I can find V(r) by $$\int E \ dl$$

Haha Phys 400? I am having similar trouble...

## 1. What is the concept of energy in coaxial cylindrical shells?

The energy in coaxial cylindrical shells refers to the potential energy stored between two concentric cylindrical shells with opposite charges. This energy is directly proportional to the amount of charge and inversely proportional to the distance between the shells.

## 2. How is the energy of coaxial cylindrical shells calculated?

The energy of coaxial cylindrical shells can be calculated using the formula U = (1/4πε0) * (Q1 * Q2) / d, where U is the potential energy, ε0 is the permittivity of free space, Q1 and Q2 are the charges on the inner and outer shells respectively, and d is the distance between the shells.

## 3. What factors affect the energy of coaxial cylindrical shells?

The energy of coaxial cylindrical shells is affected by the amount of charge on the shells, the distance between the shells, and the permittivity of free space. Additionally, the presence of any dielectric material between the shells can also affect the energy.

## 4. How does the energy of coaxial cylindrical shells relate to electric potential?

The energy of coaxial cylindrical shells is directly related to the electric potential between the shells. The electric potential is defined as the energy per unit charge, and in the case of coaxial cylindrical shells, it is equal to the energy divided by the total charge on the shells.

## 5. What are some real-life applications of the energy of coaxial cylindrical shells?

The energy of coaxial cylindrical shells has various applications in technology, such as in capacitors and high-voltage power lines. It is also used in scientific experiments to study the behavior of electric fields and their effects on different materials. Additionally, the concept of energy in coaxial cylindrical shells is also important in understanding the principles of electrostatics and electromagnetism.

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