A cylindrical capacitor consists of a solid inner conducting core with radius 0.260 cm , surrounded by an outer hollow conducting tube.?
The two conductors are separated by air, and the length of the cylinder is 10.0 cm . The capacitance is 35.5 pF .
a) Calculate the outer radius of the hollow tube.
r = ? cm
b) When the capacitor is charged to 150 V , what is the charge per unit length λ on the capacitor?
\lambda = ? C/m
- Steve4PhysicsLv 72 years agoFavorite Answer
Using the formula in the link with k (dielectric constant) = 1 for air gives:
C = 2πε₀L / ln(b/a)
Note a and b (the radii) can be in any units, providing they are the same. I’ll use cm for both. (But L must be in metres.)
35.5x10^-12 = 2π x 8.854x10^-12 x 0.100 / ln(b/0.260)
ln(b/0.260) = 2π x 8.854x10^-12 x 0.100 / (35.5x10^-12)
. . . . . . . . . = 0.1567
b/0.260 = e^0.1567
. . . . . . = 1.170
b = 0.260 x 1.170
. .= 0.304 cm (3 sig. figs.)
Q = CV
. . = 35.5x10^-12 x 150
. . = 5.325x10^-9 C
λ = Q/L
. .= 5.325x10^-9 / 0.100
. .= 5.33x10^-8 C/m (3 sig. figs.)
Check my arithmetic.