# Conservation of charge vs force

• MullaTheMech
F = \frac{1}{4\pi\epsilon_0} \frac{6}{4\pi^2}## Which is the same as saying the electron feels a force of 3.3 Newtons.Now, let's do the same thing for ball B. The electron on ball B feels the force of 4 electrons from ball A, or... ##F = \frac{1}{4\pi\epsilon_0} \frac{4}{4\pi^2}## Which is the same as saying the electron feels a force of 1.7 Newtons. So, the total force felt by the electron on ball A is... ##F = \frac{1}{4\pi

#### MullaTheMech

So I was posting questions in someones homework help and I thought I'd create my own thread instead.
Now in coulombs equation you multiply the coulombs (Q1×Q2)
Ujjwal (OP in other thread) was using 2 balls charged at 2 and 3 coulombs in one of his examples.
2×3=6
But after the balls touch they are both 2.5
2.5×2.5=6.25
This means the force will be greater after the metallic balls equal out their charge.
How can electrons (or lack of) moving from ball to ball change the force in this system? I see it in the equation but it seems fundamentally wrong to me.

Can someone help me with my misconception with force?

Force is not supposed to be conserved. then sharing charge of each other involves force as well as energy. Doing it mathematically in the brain requires nothing of the charges outside but must involve charges in our brain!

Also how do you calculate the force of attraction to something with no charge.
0C×2C=0C

Force is not something which exists in one object but is what happens between two objects.

Let'sthink said:
Force is not something which exists in one object but is what happens between two objects.
So why would the force change between the two objects? I'm picturing something like 2 situations where one has a ball of 4 electrons and a ball of 6 electrons
And another situation where there's 2 balls containing 5 electrons each.
They are both the same distance apart.
I feel intuitively that they should repel each other with the same force.
Someone want to write their thought process out?

We can have intuition and related theories of our own, but they need to be tested against actual experiment. Experiment says that the total force between two objects is not invariant with respect to the total charge but depends on the distribution of the charge. Even if we both are writing our thought process which intuition for you the final arbiter is the experiment and we both have to bow down to that!

My imagination and intuition has only been limited by my predecessors.

Well thanks for that. I wanted to be able to change my thought process.

In my line of work I'm frequently asked to do shoddy repairs and modifications. I rarely use formulas and calculations since the person that pays me won't wait for them, want them, or pay for them. I use only my intuition.

Intuitively understanding forces from different charges would help me when charging paint for example.

Would your intuition tell you that two rectangles of the same perimeter must have the same area?
For example, one can be a 2 by 6 and the second a 4 by 4 (square).
2+6=4+4 but the areas are not the same.

And back to your problem, if you move the total charge on just one object, the Coulomb force will be zero.

MullaTheMech, when you charge for painting you do not charge for the total amount of paint used only but also on the area on which you distribute it. Ther larger area you will distribute better the paint will stick!.

Ah well I'll step off the easy path then. I'll have to get to learning.

MullaTheMech said:
So why would the force change between the two objects? I'm picturing something like 2 situations where one has a ball of 4 electrons and a ball of 6 electrons
And another situation where there's 2 balls containing 5 electrons each.
They are both the same distance apart.
I feel intuitively that they should repel each other with the same force.
Someone want to write their thought process out?
Force depends on charge that a body has.The higher the charge the more the force it applies on others. If a body has 5 extra electrons it would apply a force lesser than the body which has 6 extra electrons. It is due to the fact that force just depends on the extra charges that a body has. It is not force which is to be conserved but energy. Energy is always conserved.
You know that an uncharged body cannot apply an electrical force.
IF according to you the charges are transferred from one body to another resulting in no change in force, it would imply that if all the electrons from one ball are transferred to other ball such that one ball has no electrons and other has 10 electrons it would still result into some force between them but since one ball has no charge how could a force be set up between them.
Electrostatic force ##F = \frac{1}{4\pi\epsilon_0} \frac{Q_1 Q_2}{r^2}##

Let's try this. Consider your example - the first ball (call it ball A) has 4 electrons and the second ball (call it ball B) has 6. Let's look at each of the electrons on ball A and say an electron imparts a force F on another electron: the first electron feels the force of 6 electrons from ball B, or 6F; the second one also feels the force of 6 electrons, or 6F, etc. so the 4 electrons on ball A feel in total the force 6F + 6F + 6F + 6F= 24F.

Now let's take your other example where ball A and B both have 5 electrons and again look at ball A: The first electron feels the force of 5 electrons from ball B, or 5F; the second one also feels the force of 5 electrons, or 5F, etc. so the 5 electrons on ball A feel in total the force 5F + 5F + 5F + 5F + 5F = 25F, which is a larger (EDITED) total force than in the first example.

Really this is nothing more than saying that the force depends on the product of the total charge on each ball, 4 x 6 = 6 + 6 + 6 + 6 and 5 x 5 = 5 + 5 + 5 + 5 + 5.

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MullaTheMech
You mean 25 is larger than 24, right? :)

nasu said:
You mean 25 is larger than 24, right? :)

Thank you. I corrected it. I may know Coulomb's Law but not arithmetic.

For the OP, the point of my post is that there are 25 electron-electron pairs in the second case compared with 24 in the first.

That's a great explanation for my example. Thank you.