# Correct statement about force between two charges

1. Feb 14, 2019 at 3:49 AM

### songoku

1. The problem statement, all variables and given/known data
Two conducting spheres A and B, of radii ra and rb, carry charges +Qa and - Qb respectively. The centers of the spheres are a distance d apart with d slightly greater than ra+rb. Which of the following statements about the electrostatic forces F between the spheres is true?
a. F < k QaQb/d2
b. F = k QaQb/d2
c. F > k QaQb/d2
d. F < k QaQb/(d - ra - rb)2
e. F > k QaQb/(d - ra - rb)2

2. Relevant equations
Coulomb's law

3. The attempt at a solution
My answer is B but I am considering another answer which is C because the charge on each sphere is not evenly distributed throughout the surface but will be collected to one side of the sphere. So it is B or C?

Thanks

Last edited: Feb 14, 2019 at 6:29 AM
2. Feb 14, 2019 at 6:10 AM

### haruspex

Right, but in a way that increases or reduces the attraction?

What about d and e? Could one of those be true too?

3. Feb 14, 2019 at 6:19 AM

### songoku

The center of charge distribution is not same as center of sphere anymore so the center of the charge distribution is less than d, making the attractive force bigger

The distance in the denominator is from surface to surface so it may not represents the distance from center of charge to center of charge.

Edit: I just realised that option (d) is possible because the distance between the center of charge distribution is bigger than distance from surface to surface

Last edited: Feb 14, 2019 at 6:28 AM
4. Feb 14, 2019 at 7:31 AM

### PeroK

What if $Q_a = -e$ and $Q_b = e$, where $e$ is the charge on an electron?

5. Feb 14, 2019 at 8:04 AM

### songoku

Does the amount of charge affect the answer?

Thanks

6. Feb 14, 2019 at 8:07 AM

### PeroK

What do you think? Why did I suggest this example? Do some calculations.

7. Feb 14, 2019 at 8:16 AM

### songoku

Sorry I do not know what to calculate and I do not understand the purpose of your hint.

Changing the amount of charge will change the magnitude of the force but in my opinion in this question the distance is the variable that I need to consider, not the charge.

I think changing the charge won't affect the distance or maybe not significantly.

Thanks

8. Feb 14, 2019 at 8:22 AM

### PeroK

What do you think about d)? It looks like a good answer to me, at first sight at least. Can you see why answer e) is impossible?

9. Feb 14, 2019 at 8:31 AM

### songoku

I think there are two correct answer C or D.

B is not possible because the distance needed to calculate the force is not equal to d.

E is not possible because the distance should be bigger than d - ra - rb so the force will be less than that

10. Feb 14, 2019 at 8:51 AM

### PeroK

That's not a bad answer. Technically, if there is only one unit of charge on each sphere, then those charges would end up precisely $d - r_a - r_b$ apart and you would have equality in equation d). So, technically, d) would need to be $\le$ to be correct in all cases.

I'm not sure whether the question setter intended you to think about this. If there is only one correct answer, then it must be c). It's "more correct" than d). It doesn't say "in all cases" and d) is usually true.

11. Feb 14, 2019 at 8:57 AM

### songoku

I understand.

Thank you very much for the help haruspex and perok