Question

A cylindrical capacitor has two co-axial cylinders of length $20 \,cm$ and radii $1.5\, cm$ and $1.6 \,cm$. 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 $L = 20\, cm = 20 \times10^{-2} \, m$
inner radius $r_{i}=1.5\,cm=1.5\times10^{-2}\, m$
outer radius $ r_{0}=1.6 \,cm=1.6\times10^{-2}\,m$
charge $q - 4 \, \mu C=4\times10^{-6}\, C$
Capacitance,
$C=\frac{2\pi\varepsilon_{0} L}{log_{e}\left(\frac{r_{0}}{r_{i}}\right)}=\frac{2\pi\varepsilon_{0} L}{2.3 \, log_{10} \left(\frac{r_{0}}{r_{i}}\right)}$
$=\frac{2\pi\times8.85\times10^{-12}\times20\times10^{-2}}{2.3 log_{10} \left(\frac{1.6\times10^{-2}}{1.5\times10^{-2}}\right)}\quad$
$=1.7\times10^{-10}\, F$