What Is the Potential of the Combined Water Drop?

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Homework Help Overview

The discussion revolves around the potential of a larger water drop formed by combining eight smaller charged drops, each with a radius of 1 mm and a charge of 10^(-10) Coulombs. Participants are exploring the relationships between radius, volume, and charge in this context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants question how the radius and charge change when the smaller drops combine. There is discussion about whether the radius of the larger drop can be simply calculated by summing the radii of the smaller drops, and whether the charge adds linearly.

Discussion Status

There is an active exploration of the relationships between volume, radius, and charge. Some participants have provided guidance on calculating the volume of the drops and have prompted others to reconsider their assumptions about how the radius of the combined drop is determined.

Contextual Notes

Participants express uncertainty about the connection between volume and potential, and there is a noted lack of consensus on the correct approach to determining the radius of the larger drop.

Abel I Daniel
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Homework Statement


8 Charged drops of water each of radius 1 mm and having a charge of 10^(-10) Coloumbs are combined to form a bigger drop.Determine the potential of the bigger drop.

Homework Equations


Does the radius becomes 4*10^(-3)m,when it combines?
Does the charge sum up to 9*10^(-10)?

The Attempt at a Solution

[/B]
Used the formula -V=9*10^(9)*Q/r
Got the ans as 1800 V.
 
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Abel I Daniel said:

Homework Statement


8 Charged drops of water each of radius 1 mm and having a charge of 10^(-10) Coloumbs are combined to form a bigger drop.Determine the potential of the bigger drop.

Homework Equations


Does the radius becomes 4*10^(-3)m,when it combines?
I don't think so. It's probably easier to work with the mm units that were given.
What's the volume of one rain drop?
If you combine 8 rain drops into one bigger drop, what is the volume of this larger drop? What's its radius?
Abel I Daniel said:
Does the charge sum up to 9*10^(-10)?

The Attempt at a Solution

[/B]
Used the formula -V=9*10^(9)*Q/r
Got the ans as 1800 V.
 
Mark44 said:
I don't think so. It's probably easier to work with the mm units that were given.
What's the volume of one rain drop?
If you combine 8 rain drops into one bigger drop, what is the volume of this larger drop? What's its radius?

I assume the volume to be (4/3)*(pi)*r^3,where r is 1 mm.
But what potential has to do with Volume.i am quit weak in this subject
 
Abel I Daniel said:
I assume the volume to be (4/3)*(pi)*r^3,where r is 1 mm.
Or more simply, 4/3 ##\pi##, the volume of one rain drop,
Abel I Daniel said:
But what potential has to do with Volume.i am quit weak in this subject
From the formula you wrote in post #1, the potential V is a function of the radius r.
-V=9*10^(9)*Q/r
If 8 rain drops combine into one larger drop, what's the volume of the larger rain drop? What's the radius of the larger rain drop?
 
Mark44 said:
If 8 rain drops combine into one larger drop, what's the volume of the larger rain drop? What's the radius of the larger rain drop?
i hope it adds up linearliy,that means ,radius of larger frop =8* 1mm (radius of each smaller drop)
 
Abel I Daniel said:
i hope it adds up linearliy,that means ,radius of larger frop =8* 1mm (radius of each smaller drop)
No, it doesn't.
The volumes add like you think they would, but the radius of the combined raindrop is NOT 8mm.
 
Mark44 said:
The volumes add like you think they would, but the radius of the combined raindrop is NOT 8mm.
the bigger radius becomes twice the smaller radius ie 2 mm.But what about the charge ?
 
2 mm is more like it. I'm pretty sure the charge is additive.
 
THank you Mark44,for helping me to reach to the answer.You made me think,which i already knew
 

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