Correct statement about force between two charges

[songoku]

Homework Statement

Two conducting spheres A and B, of radii r_a and r_b, carry charges +Q_a and - Q_b respectively. The centers of the spheres are a distance d apart with d slightly greater than r_a+r_b. Which of the following statements about the electrostatic forces F between the spheres is true?
a. F < k Q_aQ_b/d²
b. F = k Q_aQ_b/d²
c. F > k Q_aQ_b/d²
d. F < k Q_aQ_b/(d - r_a - r_b)²
e. F > k Q_aQ_b/(d - r_a - r_b)²

Homework Equations

Coulomb's law

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

Edit: revising choices of answer

 

[haruspex]

the charge on each sphere is not evenly distributed throughout the surface but will be collected to one side of the sphere.

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

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

 

[songoku]

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

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

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

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 realized that option (d) is possible because the distance between the center of charge distribution is bigger than distance from surface to surface

 

[PeroK]

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 biggerThe 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 realized that option (d) is possible because the distance between the center of charge distribution is bigger than distance from surface to surface

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

 

[songoku]

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

Does the amount of charge affect the answer?

Thanks

 

[PeroK]

Does the amount of charge affect the answer?

Thanks

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

 

[songoku]

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

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

 

[PeroK]

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

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?

 

[songoku]

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?

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 - r_a - r_b so the force will be less than that

 

[PeroK]

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 - r_a - r_b so the force will be less than that

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.

 

[songoku]

I understand.

Thank you very much for the help haruspex and perok