A certain cylindrical capacitor has a length of 47 cm; the inner cylindrical con

Question

A certain cylindrical capacitor has a length of 47 cm; the inner cylindrical conductor has a DIAMETER of 2.61 mm and the outer conducting shell has an inner DIAMETER of 7.90 mm. Assume the region between the conductors is vacuum. Assume that a charge of82.50 nanocoulombs is separated by the capacitor.

(a) Ignoring any possible end effects, use Gauss' Law to find an expression for the electric field in the space in between the two conductors. Then substitute values into that expression to find the electric field strength at the following locations (r represents the distance from the common central axis of the central wire and the shell)

:at r=2.187 mm: 1443392  V/m (correct)

at r=3.068 mm: 1028910.49   V/m (correct)

(b) Now integrate your expression for the electric field to find the absolute value of the potential difference between the two conductors.  

3496.0423 V (correct)

(c) Use the definition of capacitance with your answer to (b) to determine the capacitance of this cylindrical capacitor. Give your answer in nanofarads. nF

(d) What is the amount of energy stored in this capacitor when it is separating a charge of 82.50 nC?

J

(e) Find an expression for the electric energy density in the space between the two conductors. Then substitute values into that expression to find the electric energy density at the following locations

:at r=2.187 mm:   J/m3

at r=3.068 mm:  J/m3

(f) Integrate your expression from part (e) over the volume of the space between the two conductors in order to compute the total electric energy stored in the capacitor when it is separating a charge of 82.50 nC.

J

Explanation / Answer

c)0.0235 nF

d)1.44*10^-4 J

e)

:at r=2.187 mm: 0 J/m3

at r=3.068 mm: 0.0102 J/m3

f)6.507*10^-5 J

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