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Electrostatics question

2022 · 25 Jun · Shift 2 · Q70
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Electrostatics question

2022 · 25 Jun · Shift 2 · Q70

JEE MainPhysicsElectrostaticsNumerical+4 / −1
27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be ‾\underline{\hspace{2cm}}​ V.
Numerical answer
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Correct answer: 198

  1. For an isolated spherical drop, electric potential is

V=14πε0qr=kqrV = \frac{1}{4\pi\varepsilon_0}\frac{q}{r} = k\frac{q}{r}V=4πε0​1​rq​=krq​

where qqq is the charge and rrr is the radius.

  1. Let each small drop have:
  • charge qqq
  • radius rrr
  • potential V1=22 VV_1 = 22\,\text{V}V1​=22V

So,

V1=kqr=22V_1 = k\frac{q}{r} = 22V1​=krq​=22

  1. When 272727 identical drops combine:
  • total charge becomes

Q=27qQ = 27qQ=27q

  • total volume becomes 272727 times, so radius becomes

R=271/3r=3rR = 27^{1/3}r = 3rR=271/3r=3r

  1. Potential of the bigger drop:

V2=kQR=k27q3r=9kqrV_2 = k\frac{Q}{R} = k\frac{27q}{3r} = 9k\frac{q}{r}V2​=kRQ​=k3r27q​=9krq​

Using kqr=22k\frac{q}{r} = 22krq​=22,

V2=9×22=198 VV_2 = 9 \times 22 = 198\,\text{V}V2​=9×22=198V

  1. Therefore, the potential of the bigger drop is

198\boxed{198}198​

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