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1. Two conducting cyllinders have radii R and 2R. They are concentric with each other (they...

1. Two conducting cyllinders have radii R and 2R. They are concentric with each other (they share the same center). The outer cyllinder has charge q and the inner cylinder has charge −q. Both cylinders have a lenght L where L >> R. Our goal is to find the capacitance of our system.
(a) Using Gauss’s law, solve for the electric field between the cylinders.

(b) Solve for the voltage difference between the cylinders. Hint: use a path integral.

(c) Solve for the capacitance of the system.

(d) If you double the radii of each cylinder, how does the capacitance change?

(e) Solve for the energy of the system.

(f) Suppose a dielectric with constant k = 2 is placed between the cylinders. By what factor does the enerygy change?

(g) Unit check

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