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Concentric Cylindrical Insulator and Conducting Shell: An infinitely long solid insulating cylinder of radius a = 4.5 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 49.0 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 13.6 cm, and outer radius c = 17.6 cm. The conducting shell has a linear charge density λ = -0.53μC/m. What is V(P) – V(R), the potential difference between points P and R? Point P is located at (x,y) = (50.0 cm, 50.0 cm).

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\[E=(roe)(r_{a})^{2}/(2*\epsilon*\pi*r _{d}) +(\lambda/(2\epsilon \pi r _{d}))\]
I integrated from 0.5->0.7 but am not getting the right answer.

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Other answers:

where is R?
E is a constant.(I believe you can use gauss law to find the electric field--the one I got is different from yours though...take care of the volume and areas differently.) So, \(V=E\int d\vec l=E (\int dx + \int dy)\)
R (0,50)
I did use gauss's law to find electric field. The electric field I posted was correct. I know because I already answered what the electric field is. what do you mean by constant? Where is E constant?
\[-\int\limits_{0.5}^{0.7}E dl\] with E being what I posted. I replaced rd with x and dl with dx and integrated but came up with the wrong answer no matter what sign I used.
E is not a variable of x, or z. isn't E just \((something)\hat j\) in the integral here? though...yeah, that's the correct boundaries. might there be a mistake in the answer?
If he was just something then that would be saying he is constant along P to R but that is not the case. I appreciate your time, it seems no one else will help with this question.
if E was just something then that would be saaying E is...****
@TuringTest, do you think you might have some input?

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