Finding the electric field on a cylinder with a holeby PhysicsRob Tags: cylinder, electric field, gauss' law, hole, superposition 

#1
Jan2513, 02:40 PM

P: 8

1. The problem statement, all variables and given/known data
A very long, solid insulating cylinder with radius "R" has a cylindrical hole with radius "a" bored along its entire length. The solid material of the cylinder has a uniform volume charge density "ρ". In this problem, you will find the magnitude and the direction of the electric field "E" inside the hole (1) Find the magnitude and direction of the electric field of a cylinder similar to the one described above, but without the cylindrical hole. (2) Find the magnitude and direction of the electric field inside the cylindrical hole when the cylindrical hole is in the center of the charged cylinder (3)Find the magnitude and direction of the electric field inside the cylindrical hole when the center of the hole is a distance "b" from the center of the charged cylinder. 2. Relevant equations Gauss' Law 3. The attempt at a solution I solved through the first part for the solid cylinder by using a Gaussian cylinder with a radius of "r", r>R>a. I got that [itex]\vec{E}[/itex] = (R^{2}ρ)/2rε_{0} along vector "r". For the second part I thought that the field inside would be zero since if you drew a Gaussian cylinder inside the hole, wouldn't it contain no charge and thus have no electric field? For the third part I know that you need to use the idea of superposition, but I'm not really sure. 



#2
Jan2513, 03:16 PM

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#3
Jan2513, 03:50 PM

P: 8

Well for the first part I calculated that electric field for a "r" that was greater than "R", so shouldn't it be decreasing as "r" gets greater? Instead of doing this, should I calculate the electric field at the border of the cylinder?
For the second part, well then could you explain what else I could do to find the electric field inside the hole? I'm not sure what else I would do. For the third part, I'm just not that sure about how to do it. 



#4
Jan2513, 04:13 PM

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Finding the electric field on a cylinder with a hole 



#5
Jan2713, 07:30 PM

P: 8

Okay, so I'm pretty sure I have it now:
So for the first part I got E=rρ/2ε_{0} in the direction of vector "r" For the second part I got that E=0 For the third part I got that E=bρ/2ε_{0} in the direction of vector "r" Does that seem right? The only thing I'm not totally sure about now is the direction of the field in the third part. Would it be in the direction of "r" or "rb"? 



#6
Jan2713, 08:07 PM

P: 8

Oh wait, nevermind. The third part would be in the direction of just vector "b" correct? Since it doesn't depend on "r"?




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Jan2713, 09:50 PM

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