How Does the Potential of a Coalesced Drop Compare to Its Original Drops?

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SUMMARY

The discussion centers on the comparison of electric potential between multiple charged drops of salt water and a single coalesced drop. Each of the 27 original drops has a potential of V volts, leading to a total potential of 27V when considered collectively. However, when these drops coalesce into one, the potential of the new drop is V, making the original drops' potential 27 times greater than that of the single drop. The analysis confirms that the potential is measured at the surface of the drops, highlighting the differences in electric potential due to the change in configuration.

PREREQUISITES
  • Understanding of electric potential and point charges
  • Familiarity with the equation V = k * q/r
  • Knowledge of electrostatics and charge distribution
  • Basic principles of coalescence in physics
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  • Study the principles of electrostatics in detail
  • Learn about the implications of charge distribution in coalesced systems
  • Explore the concept of electric potential in different geometries
  • Investigate the behavior of charged droplets in various physical contexts
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Students of physics, particularly those studying electrostatics, as well as educators and anyone interested in the behavior of charged particles and their interactions in fluid dynamics.

captain.joco
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Homework Statement


27 drops of salt water with same radius, are each charged to a potential of V volts. They are made to coalesce into a single drop. How is the potential of a new drop compared to the potential of the original drops.

Homework Equations


V ( potential ) = k* q/r
k=1/(4∏ε.)


The Attempt at a Solution


I know that the total potential of collection of point charges is ( assuming we can take the drops as point charges ): Vtotal = k Σ q/r; so Vtotal should be 27V. Now if we add another drop and we measure the potential at the same distance as we have measure it from the original drops, the new drop will have potetntial V.
So from the ratio Vtotal/V can be seen that the original drops have a potential 27times bigger then a single new drop. Is this even nearly correct? Thanks
 
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I THINK they mean how does the potential of a single drop in isolation measured at the surface of a single drop compare with the potential of the combined drops, again measured at the surface of the combined drop. I'm guessing that because the '27' is convenient number for this problem. The question isn't very clearly worded.
 

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