# Trouble understanding *Electric Potential*

1. Mar 11, 2005

### Eternal

All day I tried to solve different kind of problems regarding electric potential and I can't get any hang of this notion. Here is a sample

Problem:

Eight droplets of water, each having radius 1,0 mm and charge 10 nC, unite into one blob. Find the electric potential of the blob!

Solution:
1)Granted that the charge is on the surface of the droplet then I understand that electric potential of one droplet is

$$\varphi=k\frac{q}{r_1}\ (k=9\cdot 10^9)$$

2) Now when all of them merge then the surface area of the spherical blob is 8 times bigger which means the radius becomes
$$r_2=\sqrt{8}\cdot r_1$$ and total charge $$Q=8q$$

So I figured that the electric potential of the blob is
$$\varphi=k\frac{Q}{\sqrt{8}\cdot r_1} \approx 255 kV$$

but the correct answer should be 3,6 kV! I checked my calculations, everything is fine, it rather seems that my reasoning is somewhat misguiding. Formulas that I'm using give the potent. energy of the unit charge in the field of charge q in the distance of r. But in this problem I equipot. surfaces or something!
Could you please show where I'm going wrong!

Thanks!

2. Mar 11, 2005

### Gamma

The volume of the blob is 8 times the volume of each droplet. That means,

$$r_2 = \sqrt[3]{r_1}$$

Potantial $$\simeq 359 kV$$ still 10 times larger than your answer.

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