Question

A copper sphere of capacitor C is dropped in the ocean. Will the capacitance of the sphere increase, decrease or remain the same? Justify.

Answer 1

Capacitance will increase.

Explanation:

For an isolated spherical conductor in a medium of dielectric constant ε_r,

C = 4πε_oε_rr

When the copper sphere is dropped in the ocean, it becomes surrounded by water, which has a very high dielectric constant (ε_r ≈ 80).

Due to polarization of water molecules, the electric field around the sphere decreases, which reduces the potential:

C = `q/V` and V = `intvecE*dvecl`

As E and V decrease, the capacitance increases.

∴ Capacitance of the sphere increases.