Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 years ago

# 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

Relevance
• 2 years ago

a)

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.)

__________________

b)

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.