Two long concentric cylindrical shells of conductors carry equal and opposite charges. The inner shell has a radius R, and a charge + Q; the outer one has a radius R2 and a charge – Q. The length of the cylinders is L. (a) Find the electric field in the region Rị

Two long concentric cylindrical shells of conductors carry equal and opposite charges. The inner shell has a radius R, and a charge + Q; the outer one has a radius R2 and a charge – Q. The length of the cylinders is L. (a) Find the electric field in the region Rị

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 68P: Two parallel conducting plates, each of cross-sectional area 400 cm2, are 2.0 cm apart and...

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Question

Two long concentric cylindrical shells of conductors carry equal
and opposite charges. The inner shell has a radius R, and a
charge + Q; the outer one has a radius R2 and a charge – Q.
The length of the cylinders is L.
(a) Find the electric field in the region Rị <r<R2,
r being the radial distance to the cylinder axis. (Hint: Use the
Gauss's law.)
(b) Find the potential difference between the shells. That is;
V(R:) - V(R2) = ?
(c) Using the results of (a) and (b), find the capacitance C as a
function of Q, L and radii R1 and R2of the cylinders.
+e
R1
R2
Now assume that there is a dielectric material in the region
between the plates with a dielectric constant k .
(d) How much energy is stored in the electric field between
the plates (not on the charges on the plates, that is, find the
energy from the electric field)?
L

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