Electric potential of concentr

In summary, the electric potential of a cylindrical conductor placed in a cylindrical conducting shell can be calculated by using Gauss' theorem to determine the E field, which depends only on the total charge density contained within the radius. In this scenario, the electric potential at a point outside of the outer shell can be found by summing the potentials of both the conductor and the shell and taking the difference between the two radii.
  • #1
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Electric potential of cylindrical conductor placed in a cylindrical conducting shell

Homework Statement




dcylcon.gif
gcylcon.gif


A cylindrical conducting shell is placed concentric with a cylindrical conductor. Assume that a total charge density λ0 = 2.60 µC/ m is placed on the inner cylinder and a total charge density λ = -2.90 µC/ m is placed on the outer one, r0 = 8.40 cm, r1 = 16.80 cm and r2 = 21.00 cm. Calculate, relative to r = 10·r0 = 84.0 cm:

[1pt] the electric potential at r = 30.80 cm.


Answer: -5.41E+03 V
(I need help figuring out HOW to get this answer, not the answer itself)




Homework Equations




V= the negative inegral of E
λ=Q/2(pi)r


The Attempt at a Solution



So far all I've done is that I've integrated E=2kλ/r and got v=(-2kλ)ln(r)+C for the conducting shell and Vo=(-2kλo)ln(ro)+C for the conductor.

I'm not really sure what to do with the question, though.

I'm thinking I could use those equations to find the potential of both the cylindrical conductor and the cylindrical conducting shell. Then what?

And for the shell, would I have to use the two radiuses to find it on the outside of the shell and the inside too? I have no idea, I need assistance haha.

Help would be appreciated.
 
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  • #2
Gauss' theorem will tell you that the E field depends only on the total charge density contained within the radius. In this case both of your points are outside of the outer shell, so none of the details of the inside matter. You can also do it by just summing the two potentials you have integrated and taking the difference between the two radii.
 
  • #3
okay, I'll give it a shot, thanks!
 

1. What is electric potential of concentration?

Electric potential of concentration is a measure of the electric potential difference across a concentration gradient. It is the difference in electric potential between two points in a solution, caused by the uneven distribution of ions or molecules with different charges.

2. How is electric potential of concentration calculated?

The electric potential of concentration can be calculated using the Nernst equation, which takes into account the concentration of ions or molecules and their charge. The equation is: E = E° - (RT/nF)ln([C]out/[C]in), where E is the electric potential, E° is the standard electric potential, R is the gas constant, T is the temperature, n is the number of electrons transferred, F is Faraday's constant, and [C]out and [C]in are the concentrations of the ion or molecule outside and inside the cell, respectively.

3. What factors affect the electric potential of concentration?

The electric potential of concentration is affected by the concentration gradient, temperature, and the charge and size of the ions or molecules involved. Changes in any of these factors can alter the electric potential of concentration.

4. What is the importance of electric potential of concentration in biological systems?

The electric potential of concentration is crucial for maintaining cellular homeostasis and proper functioning of biological systems. It is involved in processes such as nerve impulses, muscle contraction, and the transport of nutrients and waste products across cell membranes.

5. How can electric potential of concentration be measured?

The electric potential of concentration can be measured using an electrode, such as a pH electrode or an ion-selective electrode, which can detect changes in the concentration of specific ions. These electrodes are connected to a voltmeter, which measures the electric potential difference between the inside and outside of a cell.

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