Electrostatic force between to spheres

[oronanschel]

given to solid half charged sphere Insulators.

In which state the mutual net force is bigger: A/B/the same

 

[Delphi51]

No idea how to attempt it?
The force depends on two things. Look at the Coulomb force law formula to see what they are. You will find that one of them is the same for both arrangements, but the other is different. With some thought you can approximate that quantity for each situation and then the formula will tell you which results in the larger force.

 

[oronanschel]

if it was 2d then it an obv that B (because distance is shorter)
but i can't get a grasp of it 3d and could't compute either.

i tried to think what is the shape of the field of half sphere but
couldn't do it either.

the weird thing is that, the book argue that the net force is the same
and i think it is not

 

[Delphi51]

Going from A to B, you have flipped the large half-sphere so its center of charge is closer to the center of the smaller half-sphere. That will increase the force. Yes, it is difficult to figure out exactly where the center of charge is, but certainly it is in the interior of the hemisphere. That alone is sufficient to prove smaller distance for B, isn't it?