Electric Field of a Uniformly Charged Cylindrical Surface

AI Thread Summary
The discussion focuses on calculating the electric field strength vector on the z-axis from an infinitely long cylindrical surface with a surface charge density σ = A cosΦ. Participants highlight the complexity of the problem due to the angular dependence of σ, which varies across different planes. Suggestions include using polar coordinates for integration and considering Gauss's law to simplify the calculations. Clarifications are made regarding the charge distribution and its variation with respect to z. The conversation emphasizes the need to establish a clear approach to tackle the problem effectively.
erisedk
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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!
 
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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.
 
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?
 
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