If we merged 125 spherical mercury droplets having 2.5 V potential of each mercury droplet. What will be the potential of entire droplets will be?

  • Option 1)

    0.1 V

  • Option 2)

    1.0 V

  • Option 3)

    62.5 V

  • Option 4)

    4 V

 

Answers (2)
V Vakul

As we learnt in

Electric field and potential Due to various charge Distribution i) Point Charge -

Electric field and Potential at Point P due to a Point charge Q.

E= \frac{kQ}{r^{2}}    ,     V= \frac{kQ}{r}

- wherein

 

 Let radius of each small drop is r and radius of bigger drop be R.

\Rightarrow 125 \times \frac{4\pi }{3}r^{3} = \frac{4\pi }{3}R^{3}\Rightarrow R = 5r

Initial charge = q

Final Charge = 125 q

V_{i} = \frac{Kq}{r}, \ \ V_{f}= \frac{K.\left ( 125q \right )}{5r} = 25.\left ( \frac{Kq}{r} \right )

V_{f}= 62.5\ V


Option 1)

0.1 V

This option is incorrect

Option 2)

1.0 V

This option is incorrect

Option 3)

62.5 V

This option is correct

Option 4)

4 V

This option is incorrect

v' = n^{2/3} v

given, n= 125

therefore, 125^{2/3} = 25

that is, v' = 25 * 2.5 = 62.5

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