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2. Electric Potential and Capacitance
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The radius of a charged metal sphere $(R)$ is $10\,cm$ and its potential is $300\,V$. Find the charge density on the surface of the sphere
A
$2\times 10^{-3}\,CGS\,esu$
B
$4\times 10^{-3}\,CGS\,esu$
C
$6\times 10^{-3}\,CGS\,esu$
D
$8\times 10^{-3}\,CGS\,esu$
Solution
$1$ stat $\mathrm{volt}$ $=300$ $\mathrm{volt}$
$\frac{\mathrm{Q}}{\mathrm{R}}=\frac{\mathrm{Q}}{10}=1$ or $\quad \mathrm{Q}=10$ stat coulomb
$\sigma=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^{2}}=\frac{10}{4 \pi(10)^{2}}=\frac{1}{40 \pi}=8 \times 10^{-3} \mathrm{\,CGS}$ $\mathrm{esu}$
Standard 12
Physics
