A 67.0-m length of coaxial cable has an inner conductor that has a diameter of 2

Question

A 67.0-m length of coaxial cable has an inner conductor that has a diameter of 2.58 mm and carries a charge of 8.10 HC. The surrounding conductor has an inner diameter of 7.27 mm and a charge of -8.10 HC. Assume the region between the conductors is air. (a) What is the capacitance of this cable? nF (b) What is the potential difference between the two conductors? kV An air-filled parallel-plate capacitor has plates of area 2.60 cm2 separated by 1.00 mm. The capacitor is connected to a 21.0-V battery. (a) Find the value of its capacitance. pF (b) What is the charge on the capacitor? pC (c) What is the magnitude of the uniform electric field between the plates? V/m

Explanation / Answer

Given,

A = 2.6 cm^2 = 2.6 x 10^-4 m^2 ; d = 1 mm = 1 x 10^-3 m ; V = 21 V

a)we know that

C = e0 A/d

C = 8.85 x 10^-12 x 2.6 x 10^-4/10^-3 = 2.301 x 10^-12 F = 2.301 pF

Hence, C = 2.301 pF

b)We know that

Q = CV = 2.301 x 10^-12 x 21 = 48.321 x 10^-12 C = 48.321 pC

Hence, Q = 42.321 pC

c)E = V/d = 21/10^-3 = 2.1 x 10^4 N/C

Hence, E = 2.1 x 10^4 N/C

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