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

The correct option is C $1.7\times {10}^{-10}F$

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