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Electrostatics question

2021 · Q170
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Electrostatics question

2021 · Q170

NEETPhysicsElectrostaticsMCQ+4 / −1
Twenty seven drops of same size are charged at 220V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
  1. A
    1980 V
  2. B
    660 V
  3. C
    1320 V
  4. D
    1520 V
View written solutionFree

Correct answer: A

Let charge and radius of smaller drop is q and r respectively

For smaller drop, V = kqr=220 V{{kq} \over r} = 220\,Vrkq​=220V

Let R be radius of bigger drop,

As volume remains the same

(43πr3)×27=43πR3\left( {{4 \over 3}\pi {r^3}} \right) \times 27 = {4 \over 3}\pi {R^3}(34​πr3)×27=34​πR3

⇒\Rightarrow⇒ R = 3r

Now, using charge conservation,

Q = 27q

Vbig drop = kQr=k(27q)r=9(kqr){{kQ} \over r} = {{k\left( {27q} \right)} \over r} = 9\left( {{{kq} \over r}} \right)rkQ​=rk(27q)​=9(rkq​)

= 9 ×\times× 220 = 1980 V

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