Question

Metallic sphere of radius $5cm$ is surrounded by air. Dielectric strength of air is $5\times {10}^{5}V/m$ , then maximum charge that can be placed on sphere is

• A. $\frac{125}{3}nC$
• B. $\frac{1250}{4}nC$
• C. $\frac{1250}{9}nC$
• D. $\frac{125}{16}nC$

Answer 1

The correct option is C $\frac{1250}{9}nC$

$E$ near to sphere $=\frac{kQ}{R^2}$ < dielectric strength of air
$\frac{kQ}{R^2}<5\times {10}^5$
(If field exceed this dielectric strength then air will ionize & charge will leak to earth)
$\frac{9\times {10}^9\times Q}{25\times {10}^{-4}}=5\times {10}^5$
$Q=\frac{125\times 10}{9\times {10}^9}=\frac{125}{9}\times {10}^{-8}$
$=\frac{1250}{9}nC$