Question

A cylindrical capacitor has two co-axial cylinders of length $20 \,cm$ and radii $2 r$ 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. $\frac{0.1 \ln 2}{4 \pi \varepsilon_{0}} mV$
• B. $\frac{\ln 2}{4 \pi \varepsilon_{0}} mV$
• C. $\frac{10 \ln 2}{4 \pi \varepsilon_{0}} mV$
• D. $\frac{0.01 \ln 2}{4 \pi \varepsilon_{0}} mV$

Answer 1

Answer: (A)

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