Question

A cylindrical capacitor has two co-axial cylinders of length $20cm$ and radii $2r$ and $r$. Inner cylinder is given a charge $10\mu C$ and outer cylinder a charge of $-10\mu C$. The potential difference between the two cylinders will be

• A. $\frac{0.1\ln 2}{4\pi {\epsilon }_0}mV$
• B. $\frac{\ln 2}{4\pi {\epsilon }_0}mV$
• C. $\frac{10\ln 2}{4\pi {\epsilon }_0}mV$
• D. $\frac{0.01\ln 2}{4\pi {\epsilon }_0}mV$

Answer 1

Answer: (A)

$C=\frac{2\pi {\epsilon }_{0}l}{\ln \left(\frac{b}{a}\right)}$
$C=\frac{2\pi {\epsilon }_0\left(\frac{20}{100}\right)}{{\ln }^2}$
$\Delta V=\frac{10\times 10^{-6}\ln 3}{2\pi {\epsilon }_0\left(\frac{20}{100}\right)}$
$\Delta V=\frac{10^{-4}\ln 2}{4\pi {\epsilon }_0}$
$\Delta V=\frac{0.1\ln 2}{4\pi {\epsilon }_0}mV$