Question

How does the maximum $voltage\,(V)$ that can be given to a spherical conductor vary with its radius $R$ ?

• A. $V\alpha\frac {1}{R^2}$
• B. $V\alpha\frac {1}{R}$
• C. $V\alpha R$
• D. $V\alpha R^2$

Answer 1

Answer: (C)

$V\alpha R$

Answer 2

The breakdown or sparking occurs when the electric field becomes more than a particular value. Since $V= \frac{1}{4 \, \pi \, \varepsilon_0} \frac{q}{R} = \frac{1}{4 \, \pi \, \varepsilon_0} \frac{q}{R^2} R = ER$ Hence $V \propto R$ , because $E$ is constant .