Question

`n` small drops, each of radius `r` and having same charge `q` are combined to from a big drop. Find rato of capacitance, potential and stored energy in bigger drop and smaller drop.

Answer 1

Total charge on big drop: `Q=nq`
let radius of big drop be R. since volume remains same
`(4)/(3)piR^(3)=n(4)/(3)pir^(3)`
`R=n^((1//3)r`
Ratio of potantials:
`(c)/(c)=(4piin_(0)R)/(4piin_(0)r)=(R )/(r )=n^(1//3)`
Ratio of potentials:
`(V)/(v)=((1)/(4piin_(0)).(Q)/(R ))/((1)/(4piin_(0)).(q)/(r ))=((Q)/(q))((r )/(R ))=(n)/(n^(1//3))=(n)/(n^(1//3))=n^(2//3)`
Ratio of energy stored:
`(U)/(u)=(Q^(2)//2C)/(q^(2)//2c)=((Q)/(q))^(2)((c)/(c))=(n^(2))/(n^(1//3))=n^(5//3)`