A cylindrical capacitor is made of two concentric conducting cylinders. The inner cylinder has
A cylindrical capacitor is made of two concentric conducting cylinders. The inner cylinder has radius R1 = 19 cm and carries a uniform charge per unit length of λ = 30 μC/m. The outer cylinder has radius R2 = 25 cm and carries an equal but opposite charge distribution as the inner cylinder.
a. Use Gauss’ Law to write an equation for the electric field at a distance R1 < r < R2 from the center of the cylinders. Write your answer in terms of λ, r, and e0.
E=
b. Write an equation for the energy density due to the electric field between the cylinders in terms of λ, r, and e0.
u =
c. Consider a thin cylindrical shell of thickness dr and radius R1 < r < R2 that is concentric with the cylindrical capacitor. Write an equation for the total energy per unit length contained in the shell in terms of λ, r, dr, and ε0.
dU/l =
d. Calculate the energy stored per unit length in the capacitor in units of joules per meter.
U/l =
e. Calculate the electric potential difference between the outside and the inside cylinders in V.
ΔV =
f. Calculate the capacitance per unit length of these concentric cylinders in F/m.
C/l =
g. Calculate the energy stored in the capacitor per unit length, in units of J/m.
U/l =
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Given-
R1 = 19 cm
λ = 30 μC/m
R2 = 25 cm
Electric field between R1 < r < R2 is,
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