How Is the Electric Field Distributed Around Concentric Cylindrical Conductors?

[bodensee9]

Hello:

Can someone help?

I have 2 concentric cylinders which are both conductors. The inner conductor has linear charge density of 6 n C/m. The outer conductor has no net charge. The inner conductor has R of 0.015m, the distance between the inner conductor and the inner wall of the outer conductor is 0.03m, and the outer conductor has a radius of 0.065 m. I am to find the E field at all Rs.

So within the inner conductor, the R = 0.
outside the inner conductor but before you reach the inner wall of the outer conductor, the R is E*2*pi*R*L = 6e-9 * L/epsilon. So you simply that and you get 108/epsilon.
IN between the inner and outer wall of the outer conductor the E field is again 0.

But what about the E field outside the outer conductor? I know that it has to do with the ratio of the density, but I am not sure what I am doing wrong but I get the wrong answer when I say that the outer density is proportional to the radius ( = 6 * 0.065/0.015)? Any help would be great. THank you.

 

[Defennder]

Your question does not appear to be properly stated. The inner cylindrical conductor has a non-zero radius, so one would expect a surface charge density, but instead you gave a linear charge density with units C/m. Is this problem part of a larger question or is it standalone?

 

[bodensee9]

Hi,

This is the question as is given in the book. But couldn't I derive the surface density from the linear density by the following: sigma*2*pi*R = linear charge density? Where sigma is surface charge density and R is the radius of the cylinder. This is the problem. My problem is I don't see why the outside cynlinder should have an E field that is 1.46 times that of the inner E field?

 

[Defennder]

The problem with this is that it is stated at the outset that the inner cylinder is a conductor, which means we would expect the charge to be uniformly distributed over the cylindrical surface. Hence I expected a surface charge density. But instead the linear charge density is given. I don't know how to interpret this.

Secondly, assuming your interpretation of this is correct, I don't see what you mean. What does "1.46 times of the inner E-field" mean? It's clear, since the outer cylinder is uncharged and hence does not affect the E-field of the configuration that the E field outside is 6n/(2pi*epsilon*r). It's the same in the empty space between the two conductors, only that the r value is different. So what does "1.46 times" refer to?

 

[bodensee9]

That is what I would expect too. But the answer in the book is that the E field between the inner cynlinder and the inner wall of the outer cynlinder is exactly as you provided, which is 108 N/m^2. But then the answer they give for the E field outside the outer cylinder is for some strange reason 158 N/m^2?

Thanks.