Question

There are 27 drops of a conducting fluid. Each has a radius r and they are charged to a potential V₀. These are combined to form a bigger drop. Its potential will be –

• A. V₀
• B. 3V₀
• C. 9V₀
• D. 27V₀

Answer 1

Answer: (C)

9V₀

Answer 2

V_bigger = $\frac { \mathrm { kNq } } { \mathrm { R } }$ , V_smaller­ = $\frac { \mathrm { kq } } { \mathrm { r } }$

Q $\frac { 4 } { 3 }$ pR³ = N × $\frac { 4 } { 3 }$ pr³

\ R = N^1/3 r

\ V_bigger = $\frac { \mathrm { kNq } } { \mathrm { N } ^ { 1 / 3 } \mathrm { r } }$

or $\mathrm { V } _ { \text {bigger } } = \mathrm { N } ^ { 2 / 3 } \mathrm {~V} _ { \text {smaller } }$