Question

Four metal conductors having different shapes
1. A sphere
2. Cylindrical
3. Pear
4. Lightning conductor

Which shape will sustain its charge for the longest time?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

In case of spherical metal conductor the charge quickly spreads uniformly over the entire surface because of which charges stay for longer time on the spherical surface. While in case of non-spherical surface, the charge concentration is different at different points due to which the charges do not stay on the surface for longer time.

mathematically:

$chargedensity,\sigma \alpha \frac{1}{R}$

there is a possibility that charge may leak from the sharp edges.