The inner cylinder of a long, cylindrical capacitor has radius r_a and linear ch

Question

The inner cylinder of a long, cylindrical capacitor has radius r_a and linear charge density lambda. It is surrounded by a coaxial cylindrical conducting shell with inner radius r_b and linear charge density -lambda. Use Gauss's law to calculate the electric field in the space between the cylinders. Using your answer in (A), determine the potential difference between the shells. (C) Calculate the capacitance and the energy stored per unit length of this device. See Figure 25-6 and text in Resnick/Halliday/Walkeror Example 24.4 in Young/Freedman

Explanation / Answer

Make a cylindrical gaussian surface of radius r inside the shell

Flux = charge enclosed/e

E*2pi* r L= lambda*L/e

E= lambda/ 2pi*r*e =k*lambda/r

(b) potential diff = - integral of E.dr    from ra to rb

                  =k.lambda log (rb/ra)    where k=9*109     SI UNITS

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