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 18.5pC . The inner cylinder has a radius of 0.350mm , the outer one has a radius of 7.20mm , and the length of each cylinder is 17.0cmPart AWhat is the capacitance? Use 8.854

Answer 1

Answer: 3.12 * 10^12 F ( 3.12 pF)

Explanation: To calculate this capacitor of two hollow, coaxial, iron cylinders, we have to determine the potental differente between them and afeter that to use C=Q/ΔV

The electric field in th eregion rinner<r<router

By using the Gaussian law

∫E*ds=Q inside/εo

E*2*π*rinner^2*L= Q /εo

E=Q/(2*π*εo*r^2)

[Vab]=\int\limits^a_b {E} \, dr

where a and b are the inner and outer radii.

Then we have:

ΔV= 2*k*(Q/L)* ln (b/a)

replacing the values and using that C=Q/ΔV

we have:

C= L/(2*k*ln(b/a)=0.17/(2*9*10^9*3.023)=3.12 pF