Q. The insulation property of air breaks down at $E = 3 \times 10^{6}\ volt/metre$. The maximum charge that can be given to a square of diameter $5m\ $is approximately (in coulombs)
A) $2 \times 10^{- 2}$
B) $2 \times 10^{- 3}$
C) $2 \times 10^{- 4}$
D) $2 \times 10^{- 5}$
Explanation
(b) $E = \frac{1}{4\pi\varepsilon_{0}} \times \frac{q}{r^{2}} = 9 \times 10^{9} \times \frac{q}{r^{2}}$
$\therefore q = \frac{E \times r^{2}}{9 \times 10^{9}} = \frac{3 \times 10^{6} \times (2.5)^{2}}{9 \times 10^{9}} = 2.0833 \times 10^{- 3}$
$q$ 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$\ 2.0833 \times 10^{- 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.