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 12.5 pC . The inner cylinder has a radius of 0.450 mm , the outer one has a radius of 7.00 mm , and the length of each cylinder is 19.0 cm .

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

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

Explanation / Answer

(a) capacitance C = [2*pi*Eo*L]/ln(Rout/Rin)

where Rout = 7.0 mm , Rin = 0.450 mm , Eo = 8.85*10^-12 F/m

SO C = [2*3.14*8.85*10^-12*0.19]/ln(7/0.450) = 3.82 pF

(b) potential difference V = Q/C = 12.5/3.82 = 3.27 v

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