Potential of a Coalescing Water Droplet

[Satvik Pandey]

Homework Statement

1000 spherical water droplets, each of radius rand each carrying a charge q, coalesce to form a single bigger spherical drop. If v is the electric potential of each droplet and V that of bigger drop, then find \fracV/v

Homework Equations

As water is a good conductor of electricity so charges on it will be distributed on the surface.So water droplet can be regarded as spherical shell
Potential due to spherical shell is kq/r. where k is constant and q is charge on the shell and r is the distance between the centre of spherical shell and point on which P is to be calculated

The Attempt at a Solution

I am unable to understand what is meant by the potential of water droplet.I know potential at a point due to point charge,system of charge and due to continuous charge distribution.But they are calculated at point,I mean we calculate potential at point due to different charge distributions.How can we calculate potential of a body!

I want to know what is meant by( " v is the electric potential of each droplet" )this line of the question.
In thus problem any specific point is not mentioned.
I started like this
potential of smaller drop kq/r
potential of bigger drop k1000q/r
What value of should we take.

 

[ehild]

I am unable to understand what is meant by the potential of water droplet.I know potential at a point due to point charge,system of charge and due to continuous charge distribution.But they are calculated at point,I mean we calculate potential at point due to different charge distributions.How can we calculate potential of a body!

I want to know what is meant by( " v is the electric potential of each droplet" )this line of the question.
In thus problem any specific point is not mentioned.
I started like this
potential of smaller drop kq/r
potential of bigger drop k1000q/r
What value of should we take.

Note that r was used as the radius of the small droplets.
You can take the potential at any distance larger than the radius of the big droplet. The ratio would be 1000.
Or you can take the potential at the surface of a droplet, than you have to find R, the radius of the bigger one.
But it would be of more sense to determine the ratio of the potential energies.

ehild

 

[Satvik Pandey]

Note that r was used as the radius of the small droplets.
You can take the potential at any distance larger than the radius of the big droplet. The ratio would be 1000.
Or you can take the potential at the surface of a droplet, than you have to find R, the radius of the bigger one.
But it would be of more sense to determine the ratio of the potential energies.

ehild

but v/V is equal to 100 as given in book (answer)

 

[ehild]

but v/V is equal to 100 as given in book (answer)

You mean V/v = 100 , don't you?

That means the ratio of the surface values of the potential. What is the radius of the big drop that consists of 1000 droplet, with respect to r, the radius of the small ones?


ehild

 

[Satvik Pandey]

Yes I mean V/v.
So basically I need to consider surface values of potential.
Let the radius of smaller droplet be 'r' and bigger droplet be 'R'.
Vol. of smaller droplet=4/3*pi*r^3
Vol. of bigger droplet=4/3*pi*R^3
Vol.of smaller drop/Vol. of bigger droplet=1/1000
so r^3/R^3=1/1000 or R=10r.

 

[ehild]

What is the ratio of the surface potentials then?

ehild

 

[Satvik Pandey]

It is 100(V/v)

 

[ehild]

Well done!

ehild