Question

The rupture of air medium occurs at $E=3\times {10}^{6}V/m$. The maximum charge that can be given to a sphere of diameter $5m$ will be (in coulomb):

• A. $2\times {10}^{-2}$
• B. $2\times {10}^{-3}$
• C. $2\times {10}^{-4}$
• D. $2\times {10}^{-5}$

Answer 1

The correct option is B $2\times {10}^{-3}$

Given, $E_o=3\times {10}^{6}V/m;$ Diameter of sphere $=5m$

Electric field on the surface of the sphere $=\frac{KQ}{R^2}$

$E_o=\frac{KQ}{R^2}$

$Q=\frac{R^2{E}^o}{K}=\frac{6.25\times 3\times {10}^6}{9\times {10}^9}$

$=2\times {10}^{-3}C$