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2. Electric Potential and Capacitance
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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
$\frac{0.01 \ln 2}{4 \pi \varepsilon_0} m V$
Solution
(a)
$C=\frac{2 \pi \varepsilon_0 l}{\ln \left(\frac{b}{a}\right)}$
$C=\frac{2 \pi \varepsilon_0\left(\frac{20}{100}\right)}{\ln ^2}$
$\Delta V=\frac{10 \times 10^{-8} \ln 3}{2 \pi \varepsilon_0\left(\frac{20}{100}\right)}$
$\Delta V=\frac{10^{-4} \ln 2}{4 \pi \varepsilon_0}$
$\Delta V=\frac{0.1 \ln 2}{4 \pi \varepsilon_0} mV$
Standard 12
Physics
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