How do I calculate the ratio of charges for metal sphere?

[eureka_beyond]

Homework Statement

here's how the question goes:
the magnitudes of the charges on two identical small metal spheres are in the ratio 5:1. the coulomb interaction force between them is F1. if they are brought into contact and then separated to their respective original positions, the coulomb interaction force between them becomes F2. Which of the following are possible magnitudes of F1 : F2
a) 5:9
b)5:4
c)5:2

the correct answer for this question is a) and b), leaving c) incorrect

Homework Equations

coulomb's law:
F= kq1q2/r2

The Attempt at a Solution

I assume that the spheres carry 5x and x charge originally. So by coulonmb's law,
F1= k(5x)(x)/r2. After the spheres touch each other, their charges are share equally, so each of them will now have a charge of 3x. Hence, F2=k(3x)(3x)/r2. After some simplification, the ratio of F1:F2 should be 5:9. Which is the answer to a) . So I understand a), it's b) and c) that I don't understand.
furthermore, are charges always equally share? (like what I assume it to be in my attempt? or did I do something wrong?) If charges don't always have to be eqally share, even for identical spheres, then shouldn't both b) and c) be correct? (base on by guessing only)
thanks

 

[vishal007win]

you just assumed charges to be of same sign, what if one is positive and one is negative?

 

[eureka_beyond]

oh right! so that's where 4 comes from. thanks. okay, so this means that charges do share equally between identical spheres. Do charges share eqally if they're not identical?

 

[vishal007win]

no if they are not identical , charge will not be distributed equally,
Its the potential that becomes equal,
V=q/C
so if capacitance of both spheres is equal then charges shared will be equal, but if it is not the case, distribution will be uneven.

 

[rwisz]

for any help given.

I would like to commend you on your attempt to solve this problem using Coulomb's law. However, there are a few things that need to be clarified in order to fully understand the question and arrive at the correct answer.

Firstly, when two identical metal spheres are brought into contact, it does not necessarily mean that their charges will be equally shared. In fact, it is more likely that their charges will not be equally shared due to the different surface properties of the spheres. Therefore, it is not safe to assume that the ratio of charges will always be 5:5 after contact.

Secondly, the question states that the magnitudes of the charges are in the ratio of 5:1, not that one sphere has 5x charge and the other has x charge. This means that the actual charges on the spheres could be any multiple of 5 and 1, as long as their ratio is maintained. So, the initial charges could be 5q and q, where q is any number, and the ratio would still be 5:1.

Now, let's look at the possible answers. For a), the ratio of F1:F2 is 5:9. This means that the force between the spheres decreases after they are brought into contact and separated again. This is possible if the initial charges were 5q and q, and after contact, they became 4q and 2q. Therefore, a) is a possible answer.

For b), the ratio of F1:F2 is 5:4. This means that the force between the spheres actually increases after contact and separation. This would only be possible if the initial charges were 5q and q, and after contact, they became 6q and 0q. This may seem counterintuitive, but it is possible due to the redistribution of charge on the spheres. Therefore, b) is also a possible answer.

For c), the ratio of F1:F2 is 5:2. This means that the force between the spheres increases even more than in b). This would only be possible if the initial charges were 5q and q, and after contact, they became 7q and -1q. However, this is not physically possible as charges cannot be negative. Therefore, c) is not a possible answer.

In conclusion, the correct answers are a) and b) because they both represent