Three small identical bubbles of water having same charge coalesce to form a bigger bubble. Find the ratio of potentials on one initial bubble and the resultant bubble.

Solution:

Let initial radius = r

Potential on one bubble:

V₁ = kq/r

After coalescence:

Total charge = 3q

Volume conservation:

R³ = 3r³

R = 3^(1/3) r

Potential on bigger bubble:

V₂ = k(3q)/(3^(1/3) r)

V₂ = 3^(2/3) (kq/r)

Ratio:

V₁ : V₂ = 1 : 3^(2/3)

Answer:

1 : 3^(2/3)