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1. Electric Charges and Fields
easy
The insulation property of air breaks down at $E = 3 \times {10^6}$ $volt\,/\,metre$. The maximum charge that can be given to a sphere of diameter $5\,m$ is approximately (in coulombs)
A
$2 \times {10^{ - 2}}$
B
$2 \times {10^{ - 3}}$
C
$2 \times {10^{ - 4}}$
D
$2 \times {10^{ - 5}}$
Solution
(b) $E = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{q}{{{r^2}}} = 9 \times {10^9} \times \frac{q}{{{r^2}}}$
$q = \frac{{E \times {r^2}}}{{9 \times {{10}^9}}} = \frac{{3 \times {{10}^6} \times {{(2.5)}^2}}}{{9 \times {{10}^9}}} = 2.0833 \times {10^{ – 3}}$
q should be less than $2.0833 \times {10^{ – 3}}$. In the given set of options $2 \times {10^{ – 3}}$ is the maximum charge which is smaller than $2.0833 \times {10^{ – 3}}$.
Standard 12
Physics
