What Is the Ratio of Electrostatic Forces After Introducing a Third Sphere?

[Geekster]

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters. The electrostatic force acting on sphere 2 due to sphere 1 is F and the force acting on sphere 1 due to sphere 2 is -F'. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1, then to sphere 2, and finally removed. What is the ratio F'/F?

So when the thrid sphere touches the first sphere it takes with it half the total charge of sphere 1. Then touching it to sphere two it takes only 1/4 of the charge.

So now sphere 1 has 1/2 the original charge and sphere 2 has 3/4 of the original charge. According to Coulomb's law the force of sphere 1 on sphere 2 is going to be $$k|q_1q_2|/r^2$$.

So wouldn't the force of sphere 1 on sphere 2 be the same as the force of sphere 2 on sphere 1? And if that is the case, then the ratio would be -1, right?

 

[Geekster]

So did I do everything right? Or am I so bad that no one wants to respond?

 

[quicknote]

Correct, the ratio of F'/F would be -1. This is because when the third sphere is touched to the first and second spheres, it redistributes the charges and creates opposite charges on each sphere. This results in equal and opposite forces between the spheres, leading to a ratio of -1. This can also be seen mathematically by using Coulomb's law as you mentioned.

 

[kyle8921]

I would like to clarify a few things about this scenario. First, the charges on the spheres are not necessarily equal after the third sphere is brought into the picture. The third sphere takes away some charge from the first and second spheres, but the exact amount depends on the charge distribution on each sphere. So the ratio F'/F cannot be determined without knowing the specific charges on each sphere.

Secondly, the force acting on each sphere due to the other is not necessarily the same. While Coulomb's law states that the force is proportional to the product of the charges, it also depends on the distance between the spheres. So even if the charges on the spheres are equal, the force could be different if the distances between the spheres are different.

In conclusion, the ratio F'/F cannot be determined without more information about the specific charges and distances between the spheres. Additionally, the forces acting on each sphere could be different due to varying distances.