# Electric field everywhere for a hollow cylindrical conductor?

• Vitani11
In summary, the question asks for the electric field in an infinitely long, hollow, conducting cylinder with inner radius a and outer radius b, carrying a linear charge density λ. Using Gauss's law, it can be determined that the electric field is zero inside the cylinder (r<a and a<r<b) and is equal to λ/(2π∈r) outside the cylinder (r>b).
Vitani11

## Homework Statement

An infinitely long, hollow, conducting cylinder has a inner radius a and outer radius b and carries a linear charge density λ along its length. What is the electric field everywhere?

## Homework Equations

∫E⋅dA = Qenc/∈

Variables
∈ = permittivity constant
λ = linear charge density
E = electric field
r = distance to point of E field
Qenc = enclosed charge

## The Attempt at a Solution

For inside (r∠a) and in the shell (a∠r∠b) the electric field is zero. I don't know what to do for outside the shell. I think the charge is concentrated on the outer shell just as for a spherical conductor, is this true? Here is my attempt for outside.

#### Attachments

• IMG_20161202_105816.jpg
10.3 KB · Views: 548
Use Gauss's law:
∫E⋅dA = Q / ∈

E ⋅ (2πrL) = λ * L / ∈ where L denotes the imaginary Gaussian surface's length.

Therefore,

E = λ / (2π∈r)

Vitani11
That is exactly what I did in the picture. Great - thank you!

## 1. What is an electric field?

An electric field is a physical field created by electrically charged particles, such as electrons or protons. It describes the force that would be exerted on other charged particles placed in the field.

## 2. How is an electric field created in a hollow cylindrical conductor?

An electric field is created in a hollow cylindrical conductor when an electric charge is placed on the surface of the conductor. This charge creates an imbalance of positive and negative charges, resulting in an electric field inside the conductor.

## 3. Why is the electric field constant throughout a hollow cylindrical conductor?

The electric field is constant throughout a hollow cylindrical conductor because the charge on the surface of the conductor is evenly distributed. This results in an evenly distributed electric field inside the conductor.

## 4. How does the electric field inside a hollow cylindrical conductor compare to that of a solid cylindrical conductor?

The electric field inside a hollow cylindrical conductor is the same as that of a solid cylindrical conductor as long as the charge on the surface is the same. However, the electric field outside the hollow conductor is zero, while the electric field outside the solid conductor is not zero.

## 5. Can the electric field inside a hollow cylindrical conductor be changed?

Yes, the electric field inside a hollow cylindrical conductor can be changed by changing the amount of charge on the surface of the conductor. The electric field inside the conductor is directly proportional to the amount of charge on the surface.

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