Charge enclosed in cylinder question

In summary, the conversation discusses the electric field inside a circular cylinder and how to find the total charge enclosed within the cylinder. The given equation for the electric field includes constants c and b, and the medium is assumed to be free-space. The solution involves finding the surface integral of each side of the cylinder and using the equation D = epsilon*E. However, the direction of the electric field is not given, making it impossible to solve the problem.
  • #1
PassThePi
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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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  • #2
The direction of the E fierld is not given, making it impossible to answer the problem.
 

FAQ: Charge enclosed in cylinder question

What is a "charge enclosed in cylinder" question?

A "charge enclosed in cylinder" question is a physics problem that involves calculating the electric field or electric potential at a point inside or outside of a charged cylinder. The cylinder is usually assumed to be infinitely long and uniformly charged.

How is the electric field or potential calculated for a charged cylinder?

The electric field at a point inside or outside of a charged cylinder can be calculated using the electric field formula for a uniformly charged line. The electric potential can be calculated using the electric potential formula for a charged ring. These formulas take into account the charge density and distance from the center of the cylinder.

What are some real-world applications of "charge enclosed in cylinder" problems?

One real-world application of "charge enclosed in cylinder" problems is in the design of electronic devices, such as capacitors and electric motors. These devices use charged cylinders to store and manipulate electric charge. Another application is in the study of Earth's magnetic field, which can be approximated by a cylinder of charged particles.

How does the electric field or potential change when the cylinder is charged with different amounts of charge?

The electric field and potential will increase in magnitude as the charge on the cylinder increases. This is because the more charge there is, the stronger the electric field and potential will be. However, the shape and direction of the electric field and potential will remain the same.

Can the "charge enclosed in cylinder" problem be solved for non-uniform charge distributions?

Yes, the "charge enclosed in cylinder" problem can be solved for non-uniform charge distributions using calculus. The charge density function can be integrated to find the total charge enclosed in the cylinder, and then this value can be used in the electric field and potential formulas. Alternatively, numerical methods can be used to approximate the solutions for non-uniform charge distributions.

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