Electric Flow through a Cylinder Without Bases

In summary, the conversation is about how to calculate the electric flow through a cylinder without bases, with a given charge Q at one point. The final answer is Q/[epsilon0*sqrt(1+R^2/h^2)], but there seems to be a mistake in the calculation process. The suggestion is to try calculating the flux through the flat top and bottom of the cylinder and subtracting it from the total flux given by Gauss' Law. However, this method may result in a difficult integral.
  • #1
ori
28
0
http://t2.technion.ac.il/~snoop/Q.gif [Broken]
Q is at one point
R is the radius of this cylinder, it's height is 2h
the cylinder is without the bases.
how can i calculate the electric flow through it?
the final answer is Q/[epsilon0*sqrt(1+R^2/h^2)]
 
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  • #2
Why don't you try calculating the flux through the flat top and bottom of the cylinder? Then you could subtract it from the total flux given by Gauss' Law.
 
  • #3
ori said:
http://t2.technion.ac.il/~snoop/Q.gif [Broken]
Q is at one point
R is the radius of this cylinder, it's height is 2h
the cylinder is without the bases.
how can i calculate the electric flow through it?
the final answer is Q/[epsilon0*sqrt(1+R^2/h^2)]
where is my mistake:

we take ball with radius sqrt(R^2+h^2) and look on the rounded bases: the area of this ball inside the cylinder.

flow through bases / flow through all ball = bases area / all ball area

gaus: all ball flow is Q/epsilon0

all ball area is 4pi(R^2+h^2)

base area = circumference of projection of the base on y=2h * height of base
=(2pi*R)*[sqrt(R^2+h^2)-h]

2 bases area = base area * 2 = 4pi*R[sqrt(R^2+h^2)-h]

flow through bases=bases area*flow through all ball / all ball area=
= 4pi(R^2+h^2)Q/(epsilon0 4pi*R[sqrt(R^2+h^2)-h])=
Q(R^2+h^2)/(epsilon0 *R[sqrt(R^2+h^2)-h])

now that's not like that right answer, coz we can assign r=1 h=1
my answer qives 2/(sqrt(2)-1) * Q/epsilon0 = 2(1+sqrt(2)) * Q/epsilon0
right answer gives 1/sqrt(2) * Q/epsilon0
 
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  • #4
Tide said:
Why don't you try calculating the flux through the flat top and bottom of the cylinder? Then you could subtract it from the total flux given by Gauss' Law.
we get too hard integral at that case:
S r^2/(r^2+h^2)^(3/2) dr
or something like that
 
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1. What is the concept of electric flow through a cylinder without bases?

The concept of electric flow through a cylinder without bases refers to the movement of electric current through a cylindrical object that does not have any end caps or bases. This can occur in a variety of situations, such as when electricity is being transmitted through a wire or a pipe.

2. How does electric flow through a cylinder without bases differ from other methods of electric flow?

Unlike other methods of electric flow, such as through a circuit or a closed loop, electric flow through a cylinder without bases does not have a definite beginning or end point. Instead, the electric current flows continuously through the entire length of the cylinder.

3. What factors affect the flow of electricity through a cylinder without bases?

The flow of electricity through a cylinder without bases can be affected by several factors, including the conductivity of the material the cylinder is made of, the voltage of the electricity, and the diameter and length of the cylinder.

4. How is the flow of electricity through a cylinder without bases measured?

The flow of electricity through a cylinder without bases is typically measured in terms of current, which is the rate at which electric charge flows through the cylinder. This can be measured using an ammeter, which is a device that detects and measures the amount of current passing through a circuit.

5. What are some real-world applications of electric flow through a cylinder without bases?

Electric flow through a cylinder without bases has several practical applications, such as in the transmission of electricity through power lines, the flow of liquid or gas through pipes, and the movement of electrons through a wire in an electrical circuit. It is also used in various industries, including manufacturing, transportation, and energy production.

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