Question

A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.

Answer 1

a) the formula for the capacitance of the capacitor constructed of two coaial cylinders of the same length can be given as:
$C=\frac{2{\epsilon }_{0}L}{\ln \left(\frac{R_2}{R_1}\right)}$
$\Rightarrow C=\frac{e\times 3.14\times 8.85\times {10}^{-2}\times 1{-}^{-1}}{\ln 2}$ $[\ln 2=0.6932]$

$\Rightarrow C=80.17\times {10}^{-13}$
$\Rightarrow C=8pF$
b) Same as $\frac{R_2}{R_1}=\frac{8}{4}=2$ is same as in given in part (a):
$C=8pF$