A capacitor is made from two hollow, coaxial, iron cylinders, one inside the oth

Question

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is 10.0 pC . The inner cylinder has a radius of 0.250 mm , the outer one has a radius of 5.40 mm , and the length of each cylinder is 25.0 cm .

Q1) What is the capacitance? (Use 8.854×1012 F/m for the permittivity of free space.)

Q2) What applied potential difference is necessary to produce these charges on the cylinders?

Explanation / Answer

a) C = 2 pi e0 L / ln(b/a)

= (2 pi * 8.854 * 10-12 * 25 * 10-2) / (ln (5.4 / 0.250))

capacitance C = 4.53 * 10-12 F = 4.53 pF

b) Q = C V

potential difference V = Q / C

= (10 * 10-12) / (4.53 * 10-12)

potential difference V = 2.21 V

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