Charge enclosed in cylinder question

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SUMMARY

The discussion focuses on calculating the total charge enclosed within a circular cylinder with a given electric field expression, E = Az[(-c/h)+(b/6(epsilon zero)(3z^2 - h^2)]. The constants c and b are part of the problem, and the medium is specified as free-space. The participant initially attempted to solve the problem using surface integrals but encountered difficulties due to the unspecified direction of the electric field. Ultimately, they concluded that the lack of direction makes it impossible to solve the problem definitively.

PREREQUISITES
  • Understanding of electric fields and Gauss's law
  • Familiarity with surface integrals in electromagnetism
  • Knowledge of free-space permittivity (epsilon zero)
  • Basic calculus for evaluating integrals
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  • Study Gauss's law and its applications in cylindrical coordinates
  • Learn about electric field calculations in free-space environments
  • Explore surface integrals and their role in electromagnetism
  • Investigate the implications of electric field direction on charge calculations
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Students studying electromagnetism, physics educators, and anyone involved in solving problems related to electric fields and charge distributions in cylindrical geometries.

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Homework Statement


The electric field inside a circular cylinder of radius r = a and height z = h is given by: E = Az[(-c/h)+(b/6(epislon zero)*(3z^2 - h^2)
where c and b are constants. Assuming the medium within the cylinder is free-space, find the total charge enclosed within the cylinder.

Homework Equations


Qtot = int(int(D*ds)) = int(int(int(rho*dv)))
D = epsilon*E

The Attempt at a Solution


Surface integral of each side (1-top, 2-side, 3- bottom)
1 & 3 = 0
2 = h*pi*r^3

not sure what to do from here?***Nevermind, I figured it out I think. I'll post the solution if anybody wants it.
 
Last edited:
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The direction of the E fierld is not given, making it impossible to answer the problem.
 

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