Question

The insulation property of air breakdown is $3 \times 10^6 V/m$. Maximum charge in coulomb that can be given to a sphere of radius 10 cm is approximately

• A. $2 \, \mu C$
• B. $4.3 \, \mu C$
• C. $3.3 \, \mu C$
• D. $5.4 \, \mu C$

Answer 1

Answer: (C)

$3.3 \, \mu C$

Answer 2

Here, $E_{max} = 3\times10^{6} V m ,$
$r = 10 cm = 0.1 m$
As $E = \frac{1}{4\pi \varepsilon_{0}} \frac{q}{r^{2}}$
$\therefore \, \, q_{max } = E_{max} \times 4\pi \varepsilon_{0}r^{2}$
$\, \, \, \, \, \, \, \, \, \, \, = \frac{3\times 10^{6} \times \left(0.1\right)^{2}}{9\times 10^{9}} = 3.3 \mu C$