Charge enclosed in cylinder question

In summary, the electric field inside a circular cylinder can be calculated using the given formula and assuming the medium is free-space. To find the total charge enclosed within the cylinder, the surface integral can be used and the result is h*pi*r^3.
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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?
***I finally figured it out. Let me know if you need the answer.
 
Last edited:
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  • #2


Great job! It looks like you were able to use the surface integral to find the total charge enclosed within the cylinder. Keep up the good work!
 

FAQ: Charge enclosed in cylinder question

What is the formula for calculating the charge enclosed in a cylinder?

The formula for calculating the charge enclosed in a cylinder is Q = ρπr²h, where Q is the charge, ρ is the charge density, r is the radius of the cylinder, and h is the height of the cylinder.

How is the charge density of a cylinder defined?

The charge density of a cylinder is defined as the amount of charge per unit volume, represented by the symbol ρ. It is typically measured in units of coulombs per cubic meter (C/m³).

Can the charge enclosed in a cylinder be negative?

Yes, the charge enclosed in a cylinder can be negative. This would occur if the charge density is negative, meaning there is a net negative charge within the cylinder.

What does it mean for the charge enclosed in a cylinder to be zero?

If the charge enclosed in a cylinder is zero, it means that the net charge within the cylinder is zero. This could occur if there are equal amounts of positive and negative charge within the cylinder, or if there is no charge at all.

How does the charge enclosed in a cylinder affect the electric field inside the cylinder?

The charge enclosed in a cylinder affects the electric field inside the cylinder by creating a radial electric field that points towards or away from the center, depending on the sign of the charge. The strength of the electric field also varies with the distance from the center of the cylinder.

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