Calculating Changes in Coulomb's Law for Charged Spheres

[hallowon]

Homework Statement

Two charged spheres, 10.0 cm apart, attract each other with a force of magnitude
3.0 x10^-6 N. What force results from each of the following changes, considered
separately?

An uncharged, identical sphere is touched to one of the spheres and is then
taken far away.

Homework Equations

Coulomb's law
F= Kq1q2/r^2

The Attempt at a Solution

I don't know where to begin I'm sorry :(

 

[lubuntu]

You seems to be leaving out part of the problems, they don't make an awful lot of sense as stated.

 

[RoyalCat]

Let's start the question from the beginning. If this is how the question was presented then I think we are to assume that the two spheres were identically charged at the onset. It doesn't make much difference to the core of the matter whether we assume this or not. (I think we are, since it doesn't specify later which one of the spheres is touched by the uncharged sphere)

If the spheres are non-conducting then it is safe to assume that nothing happens as no charge transfer is possible (Or at least none we know how to account for at this level).

So let's assume that all spheres in question are conducting but that the charge distribution remains spherical.

What happens when you allow two conducting spheres to touch? How does that change their charge distribution?
(I'm not sure whether you're expected to consider the effect of the second sphere)

 

[hallowon]

isn't there a transfer of electrons? though i forgot to what extent

From what the question says there are already 2 charge spheres separated at that distance and such. An uncharged sphere is brought to one of them in contact, and is then removed. I am now asked to find magnitude of force after that.

 

[RoyalCat]

When the two spheres touch, it is as though they are one big conductor. Once you reach equilibrium, what does that say about the charge distribution and about the potential of this one big conductor?

 

[hallowon]

since they are identical masses wouldn't charge distrubution be 1/2? I think

 

[RoyalCat]

since they are identical masses wouldn't charge distrubution be 1/2? I think

That's good intuition, but please follow my questions, since once the spheres are not identical, you won't be able to just say that the charge is evenly distributed. ;)

 

[hallowon]

well it does say there identical though, and i don't really get what you mean about the potential of the conductor. Wouldn't they just repel to each other after equilibirum err rather at?

 

[RoyalCat]

well it does say there identical though, and i don't really get what you mean about the potential of the conductor. Wouldn't they just repel to each other after equilibirum err rather at?

That's irrelevant though, since you're pressing them up against each-other.
I'll ask again, what can you say about the charge distribution and potential of a conductor?

 

[hallowon]

at equilibrium the charges are distrubuted evenly and the potential of the conductor remains constant, while the electric field around it is zero

 

[RoyalCat]

at equilibrium the poential of a conductor is zero, and the charges are distrubuted evenly

That is incorrect. At equilibrium, the $$\vec E$$ field inside a conductor is zero.

Since $$E=-\frac{dV}{dx}$$ (In one dimension) that means that there is no change in potential inside a conductor.
A conductor is an equi-potential volume and the charges line up along its edge. They are not distributed evenly, but rather, in such a way as to negate the external field so the field inside the conductor is 0.

 

[hallowon]

so because there is no change in potential the force remains unaffected?

 

[RoyalCat]

so because there is no change in potential the force remains unaffected?

No, the potential inside a conductor is constant and the same throughout the conductor. So what does that tell us about our "big conductor" consisting of the two identical spheres?

 

[hallowon]

can i assume that their charge distrubtion would be identical, and e the charges line up in a way that negates the filed inside of it, And since the the charges are alikeat the edges, they would repel each other?

 

[RoyalCat]

can i assume that their charge distrubtion would be identical, and e the charges line up in a way that negates the filed inside of it, And since the the charges are alikeat the edges, they would repel each other?

Again, that may be true, but it is irrelevant. What's relevant is that the potential throughout the entire conductor would be the same! (:

What's the potential of a charged sphere?

Consider the two situations.

One where one sphere of radius $$R$$ has a charge of $$q_0$$ on it (You can calculate $$q_0$$ from the data) and potential $$V_0$$ (You can calculate this as well) and the other where the two spheres of equal radius $$R$$ have charges $$q_1, q_2$$ on them with an equal potential $$V$$

$$q_0=q_1+q_2$$

 

[hallowon]

umm hmm would it be 324 J/C >.> , i think i messed up:/