A cylindrical capacitor consists of a solid inner conducting core with radius 0.

Question

A cylindrical capacitor consists of a solid inner conducting core with radius 0.270cm , surrounded by an outer hollow conducting tube. The two conductors are separated by air, and the length of the cylinder is 14.0cm . The capacitance is 37.5pFpart

part a) Calculate the outer radius of the hollow tube. in terms of cm

partb) When the capacitor is charged to 130V , what is the charge per unit length ? on the capacitor? in terms of C/m

When the capacitor is charged to 130V , what is the charge per unit length ? on the capacitor?

pp

Explanation / Answer

Capacitance/unit length of a long cylinder is

C/L = (2??r??) / (ln (b/a))

b is radius of outside conductor

a is radius if inside conductor

?? is 8.8542e-12 F/m

?? is dielectric constant (vacuum = 1)

C = 37.5pF = (0.14)(2?*8.85e-12) / (ln (b/a))

ln (b/a) = 0.2075

b/a = 1.23

b = 1.23x0.27 = 0.3321 cm

b)

Second half, use Q = CV

Q = 37.5 x 10^-12 x 130 = 4.875 x 10^-9 C

Charge per unit length ? = (4.875 x 10^-9 C)/0.14 = 3.48 x10^-18 C/cm

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