Question

A cylindrical capacitor has two co-axial cylinders of length $20cm$ and radii $1.5cm$ and $1.6cm$. The outer cylinder is earthed and inner cylinder is given a charge of $4\mu C$. The capacitance of the system is (neglect end effects)

• A. $2.8\times 10^{-8}F$
• B. $4.2\times 10^{-14}F$
• C. $1.7\times 10^{-10}F$
• D. $3.4\times 10^{-12}F$

Answer 1

Answer: (C)

Here, length $L=20cm=20\times 10^{-2}m$
inner radius $r_i=1.5cm=1.5\times 10^{-2}m$
outer radius $r_0=1.6cm=1.6\times 10^{-2}m$
charge $q-4\mu C=4\times 10^{-6}C$
Capacitance,
$C=\frac{2\pi {\epsilon }_{0}L}{lo{g}_e\left(\frac{r_0}{r_i}\right)}=\frac{2\pi {\epsilon }_{0}L}{2.3lo{g}_{10}\left(\frac{r_0}{r_i}\right)}$
$=\frac{2\pi \times 8.85\times 10^{-12}\times 20\times 10^{-2}}{2.3lo{g}_{10}\left(\frac{1.6\times 10^{-2}}{1.5\times 10^{-2}}\right)}$
$=1.7\times 10^{-10}F$