Q. The electric strength of air is 2$\times 10^{7}$ NC$^{-1}$. The maximum charge that a metallic sphere of diameter 6 mm can hold is
A) 3 nC
B) 20 nC
C) 1.5 nC
D) 2 nC
Explanation
(d) $R = 3\ mm = 3 \times 10^{- 3}\ m$
As $E = \frac{Q}{4\pi\varepsilon_{0}R^{2}}$
$\therefore Q = 4\pi\varepsilon_{0}R^{2}E$
As maximum value of $E = 10\%$dielectric strength
$\therefore E = 10\%\ of\ 2 \times 10^{7} = 2 \times 10^{6}$NC$\ ^{- 1}$
$Q = \frac{1}{9 \times 10^{9}}\left( 3 \times 10^{- 3} \right)^{2} \times 2 \times 10^{6}$
$= 2 \times 10^{- 9}C = 2nc$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.