Question

Which of these has the highest capacitance, assuming the spheres to be metallic and of same shape and size in all the cases?

• A. An isolated sphere
• B. An isolated charged sphere
• C. Two spheres placed at a separation of 2 m
• D. Two spheres placed at a separation fo 5 m.

Answer 1

The correct option is C Two spheres placed at a separation of 2 m

Obviously, two conductors placed close to each other will have more capacity to store charge as compared to its isolated version.

Also note that it doesn't matter if the conductor is charged or not because the capacitance is independent of Q and depends only upon its geometrical shape, size and what's inside it.

Now as the separation is decreased, evidently the capacitance will increase. Thus two spheres placed at lower separation will have more capacity to store charge.

Capacitance of a sphere $=4\pi {ϵ}_{0}r$

Capacitance of spheres sepearated by a distance 'r' is $=4\pi {ϵ}_{0}ab$