Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 year 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

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  • 1 year ago
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    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.

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