Electric Potential at Cylinder Center: Calculating Error

[brichugh]

A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder?

I use eta = Q/A = Q/2piRL

dq = (eta)*dA = Q/(2piRL)*2piRdL

dV = 1 / 4 pi epsilon 0 * dq/r where r = sqrt(L^2+R^2)

V = Q/(4*pi*epsilon_0)*int(dL/(sqrt(L^2+R^2)))

This seems to be incorrect can someone tell me where I have gone wrong?

Thanks in advance.

 

[Gamma]

You are missing an H = height of the cylinder in the denominator of the equation.


Also limits of the integral (-h/2 -> h/2) if your referance point is the middle of the cylinder.

 

[wais]

There are a few potential sources of error in your calculation. Firstly, the expression for dq should be dq = eta * dL, since dA is equal to R * dL for a cylindrical shell. Secondly, the integral should be taken over the entire length of the cylinder, not just a small portion of it. Additionally, it is important to consider the direction of the electric field at the center of the cylinder, since the potential will depend on the direction of the field. It may be helpful to draw a diagram and carefully consider the geometry and direction of the electric field lines. I would also recommend double checking the units and constants used in the calculation to ensure they are consistent. Overall, it is always a good idea to double check your work and carefully consider the physical meaning of the equations being used.