Electric Field of a Uniformly Charged Cylindrical Surface

In summary, the problem involves finding the electric field strength on the z axis of an infinitely long cylindrical surface with a uniform surface charge density of A cosΦ. The charge density varies with the polar angle Φ and thus is different on different planes passing through the z = 0 axis. To solve this, one can use cylindrical coordinate system and Gauss's law. The approach involves finding the electric field components on the x=0 and y=0 axes and integrating them over the entire circle and z axis. It is also important to consider the charge distribution and its variation with z.
  • #1
erisedk
374
7

Homework Statement


An infinitely long cylindrical surface of circular cross-section is uniformly charged lengthwise with the surface density σ = A cosΦ where Φ is the polar angle of the cylindrical coordinate system whose z axis coincides with the axis of the the given surface. Find the magnitude and direction of the electric field strength vector on the z axis.

Source: Irodov

Homework Equations

The Attempt at a Solution


Since σ depends only on Φ, according to cylindrical coordinate system, σ is different on different planes that pass through z = 0. I just don't know where to begin, I looked up the answer and it didn't make sense to me very much.
Please just tell me how to start!
 
Physics news on Phys.org
  • #2
On axes x,y make the expretion of electric field components E_x, E_y for the field on the x=0, y=0 and take integrals to whole circle and z. May polar coordinates be more useful.
Also may Gauss's law be useful.
 
  • #3
erisedk said:
Since σ depends only on Φ, according to cylindrical coordinate system, σ is different on different planes that pass through z = 0.
Don't you mean through r=0?
Consider a section through it at some value of z. What does the charge distribution look like? Does it vary with z?
 

Related to Electric Field of a Uniformly Charged Cylindrical Surface

What is a cylindrical charged surface?

A cylindrical charged surface is a two-dimensional object with a cylindrical shape that has a net electrical charge. This means that the surface has either an excess or deficiency of electrons, resulting in an electric field around it.

How is the electric field calculated for a cylindrical charged surface?

The electric field for a cylindrical charged surface can be calculated using the formula E = σ/2ε, where E is the electric field intensity, σ is the surface charge density, and ε is the permittivity of the surrounding medium.

What is the significance of the surface charge density for a cylindrical charged surface?

The surface charge density is a measure of the amount of electric charge per unit area on the surface of the cylinder. It determines the strength of the electric field and how it spreads out from the surface.

How does the electric field vary with distance from a cylindrical charged surface?

The electric field intensity decreases as the distance from the surface increases. This is because the electric field spreads out as it moves away from the surface, resulting in a weaker field at a greater distance.

What are some real-life applications of cylindrical charged surfaces?

Cylindrical charged surfaces are commonly used in electrostatic precipitators, which are devices that remove particles from a gas stream using an electric field. They are also used in particle accelerators, electron microscopes, and other scientific instruments. Additionally, cylindrical charged surfaces can be found in everyday objects such as capacitors and batteries.

Similar threads

Charge upon a parallel plate capacitor
    • Introductory Physics Homework Help
Replies
18
Views
2K
Electric Field Inside Cylindrical Capacitor
    • Introductory Physics Homework Help
Replies
2
Views
1K
(Help) Surface charge density (σ) for particle to hit plate...
    • Introductory Physics Homework Help
Replies
4
Views
282
Investigating the Charge Distribution on a Bulging Sphere
    • Introductory Physics Homework Help
Replies
18
Views
1K
Direction of electric field vector on the surface of charged conductor
    • Introductory Physics Homework Help
Replies
9
Views
304
Charge on inner/outer surfaces of two large parallel conducting plates
    • Introductory Physics Homework Help
Replies
11
Views
489
Help me find the electric field vector
    • Introductory Physics Homework Help
Replies
24
Views
2K
Surface Current and Electric Field
    • Introductory Physics Homework Help
Replies
1
Views
784
Electric Field Inside a Gaussian Surface with Point Charge q
    • Introductory Physics Homework Help
Replies
4
Views
1K
Charge on a particle above a seemingly infinite charge plane
    • Introductory Physics Homework Help
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top