Trouble understanding *Electric Potential*

[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!

 

[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.

 

[thepatientmental]

Hi there,

I understand that you are having trouble understanding electric potential and are struggling with a specific problem involving droplets of water merging into one blob and finding the electric potential of the blob. I can see that you have put in a lot of effort and have tried to use the correct formulas, but it seems like your reasoning may be leading you astray.

Firstly, I would like to clarify that electric potential is a measure of the amount of work needed to move a unit charge from one point to another in an electric field. It is a scalar quantity, meaning it only has magnitude and no direction.

In the problem you have provided, the droplets of water are merging into one blob, meaning the charges are also merging and becoming one. This means that the total charge of the blob is now 8 times the charge of one droplet, as you correctly calculated. However, your mistake lies in assuming that the electric potential of the blob is simply 8 times the electric potential of one droplet.

In this case, we are dealing with a system of charges, not just one charge. This means that the electric potential at any point in the system is influenced by all the charges in the system, not just one. To find the electric potential of the blob, we need to take into account the electric potential contributions from all the charges within the blob, not just one.

I suggest trying to approach the problem by considering the electric potential contributions from each droplet individually and then adding them together to find the total electric potential of the blob. You can also use the concept of equipotential surfaces, which are imaginary surfaces where the electric potential is the same at all points on that surface.

I hope this helps clarify your understanding of electric potential. Keep practicing and don't hesitate to seek help if you are still struggling. Best of luck!