# Electric field in a hollow cylinder

• magnifik

#### magnifik

An infinitely long thick hollow cylinder has inner radius Rin and outer radius Rout. It has a non-uniform volume charge density, ρ(r) = ρ0r/Rout where r is the distance from the cylinder axis. What is the electric field magnitude as a function of r, for Rin < r < Rout?

for this problem, when you find qinside, do you integrate from Rin to r or from Rin to Rout? I'm confused because i would have expected it to be the latter, but in the solutions they integrate from Rin to r. can someone please explain this?

also, if you try to find the e-field where r > Rout, do you integrate from r to Rout?

Solution is here (problem II):
http://www.physics.gatech.edu/~em92/Classes/Fall2011/2212GHJ/main/quiz_help/200908/q2s.pdf

Last edited by a moderator:
Just use Gauss' theorem. The surface has radius r, and
q(inside) is whatever's inside!

rude man said:
Just use Gauss' theorem. The surface has radius r, and
q(inside) is whatever's inside!

since in the example in the document it asks for Rin < r < Rout.. why does it integrate from Rout to r??

It doesn't. It integrates from Rin to r.

rude man said:
It doesn't. It integrates from Rin to r.

but why not Rin to Rout?

Because ity asks for the field at Rin < r < Rout, not AT Rout.

## 1. What is an electric field in a hollow cylinder?

The electric field in a hollow cylinder refers to the distribution of electric charges within a cylindrical shell. This electric field is typically measured in units of volts per meter (V/m) and is perpendicular to the surface of the cylinder at all points.

## 2. How is the electric field in a hollow cylinder calculated?

The electric field in a hollow cylinder can be calculated using the formula E = Q/(2πε₀L), where Q is the charge enclosed within the cylinder, ε₀ is the permittivity of free space, and L is the length of the cylinder. This formula is derived from Gauss's law.

## 3. What factors influence the strength of the electric field in a hollow cylinder?

The strength of the electric field in a hollow cylinder is influenced by the charge enclosed within the cylinder, the permittivity of the material inside the cylinder, and the length of the cylinder. The electric field also decreases as the distance from the center of the cylinder increases.

## 4. Can the electric field in a hollow cylinder be negative?

No, the electric field in a hollow cylinder cannot be negative. This is because the electric field is a vector quantity and is always directed away from positive charges and towards negative charges. Since a hollow cylinder contains no net charge, the electric field will always be positive or zero.

## 5. What are some real-world applications of the electric field in a hollow cylinder?

The electric field in a hollow cylinder has various applications in different fields of science and technology. For example, it is used in the design of capacitors for storing and regulating electrical energy. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI) to create detailed images of the human body. Additionally, the electric field in a hollow cylinder is utilized in particle accelerators to generate and manipulate charged particles for scientific research.