Calculating Potential of Coalescing Charged Drops - Mathematics Problem Solving

[Abhishekdas]

Electric potential...

Homework Statement

1000 drops of same size are charged to a potential of 1V each. If they coalesce to form a single drop find its potential...

Homework Equations

The Attempt at a Solution

Here what potential are they talking about?...A drop of liquid will have different potentials at various places...Assuming the drop like a sherical metal (where potential is same throughout) i tried the sum...taking a chrage q on each the potental =kq/r whre r is the radius...when they coelesce radius become 10 times but charge is thousand times so potential becomes 100 times so ans is 100 V which is correct...but i am not convinced as i took it to be a conducting sphere...

 

[anathema]

and a drop of liquid is not a conducting sphere...

Hello, thank you for your question. In this scenario, we are assuming that the drops are charged with the same type of charge and are coalescing to form a single drop. Therefore, we can treat the resulting drop as a conducting sphere with a total charge of 1000q (where q is the charge on each individual drop). Since the potential of a conducting sphere is constant throughout, we can use the formula V = kQ/R, where Q is the total charge and R is the radius of the sphere. Plugging in the values, we get V = k(1000q)/10R = 100V. Therefore, the potential of the resulting drop is indeed 100V. I hope this helps clarify your doubts.