The insulation property of air breaks down at `E=3xx10^(6) "volt"//meter`. The maximum charge that can be given to a sphere of diameter `5m` is approximately (in coulombs)

Options

A. 3 nC
B. 20 nC
C. 1.5 nC
D. 2 nC

Answer

D

Explanation

Here, `R = 3 mm = 3xx10^(-3)m`
`"As, "E=(Q)/(4pi epsilon_(0)R^(2)) or Q=4pi epsilon_(0)R^(2)E`
For the maximum value of `E=10%` dielectric strength
`therefore" E"=10%" of " 2xx10^(7)=2xx10^(6)NC^(-1)`
`Q=(1)/(9xx10^(9))(3xx10^(-3))^(2)xx2xx10^(6)`
`=2xx10^(-9)C=2nC`