How Do You Calculate Electric Potential Difference in a Coaxial Cable?

[physicsfun]

Homework Statement

The diagram above shows a coaxial cable. The inner conductor has radius a = 0.0025 m. The outer conductor is a cylindrical shell with inner radius b = 0.0075 m, and outer radius c = 0.008 m from the center. Both conductors are coaxial. For every length L = 10 m of cable, there is a total charge q = 2.8e-008 C on the inner conductor and a total charge of Q = -5.6e-006 C on the outer conductor.

Determine the electric potential difference between the labeled points A and B.

The Attempt at a Solution

I'm a bit confused but I took a stab at the problem. First of all, I know that electric potential = V = kq/r... Also, I know that since the electric field is zero within the second conductor I would essentially only be calculating the difference in electric potential between point A and the inner surface of the outer conductor. So what I did was I calculated K
*charge enclosed/r for the two points and found the difference... I can't seem to get the answer. Am I doing this completely wrong? Does q even stand for the charge enclosed? Thanks a lot for any help... it will be appreciated greatly!

 

[jbsteele]

The electric potential difference between points A and B can be determined by calculating the charge enclosed at each point and then subtracting the two electric potentials. To calculate the charge enclosed, we can use the equation q = Q/L, where Q is the total charge for a length L of the cable. Therefore, for a length L = 10 m, the charge enclosed at point A is q = 2.8e-008 C, and the charge enclosed at point B is Q = -5.6e-006 C. Now, we can calculate the electric potential difference between points A and B using the equation V = kq/r, where k is the Coulomb's constant, q is the charge enclosed, and r is the distance from the point of interest to the center of the cable. For point A, the electric potential is V = (8.99x10^9)(2.8e-008 C)/(0.0075 m) = 381.07 V. For point B, the electric potential is V = (8.99x10^9)(-5.6e-006 C)/(0.008 m) = -694.5 V. Therefore, the electric potential difference between points A and B is V = -694.5 V - 381.07 V = -1,075.57 V.

 

[nlightner]

Hello, thank you for reaching out for help with this problem. First of all, it is important to note that the electric potential difference between two points is not affected by the charge enclosed within the conductor. The equation V = kq/r is used to calculate the electric potential at a point due to a single point charge, but in this case we are dealing with a distribution of charge along the inner and outer conductors.

To solve this problem, we can use the formula V = kQ/r, where Q is the total charge on the conductor and r is the distance from the center of the conductor. We can also use the fact that the electric potential difference between two points is the difference in electric potential at those two points.

So, for point A, the electric potential would be V_A = k(2.8e-008)/0.0025 = 1.12e-005 V. For point B, the electric potential would be V_B = k(-5.6e-006)/0.008 = -7.0e-004 V. Therefore, the electric potential difference between points A and B would be V_B - V_A = -7.0e-004 - 1.12e-005 = -7.1e-004 V.

I hope this helps clarify things. If you have any further questions, please don't hesitate to ask.