Two equally charged soap bubbles of equal volume are joined together to form a larger bubble . If each bubble had a potential V, find the potential of the resultant bubble.

Explanation

Let the radius of the smaller bubble be r and that of the larger bubble be R. Charge of each bubble = q
According to the question,
`4/3 pi R^(3) = 2 cdot 4/3 pir^(3) or, R = 2^(1//3) cdot r`
Potential of each soap bubble,
`V = q/r or, q = Vr`
`:.` Potential of the larger bubble
`=("total charge")/("radius") = (2q)/R = (2Vr)/R = (2Vr)/(2^(1//3)r) = 2^(2/3)V`.