Electrostatic force between to spheres

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The discussion revolves around the electrostatic force between two solid half-charged insulating spheres. Participants analyze how the distance between the centers of charge affects the mutual force, referencing Coulomb's law. While one view suggests that flipping the larger half-sphere closer to the smaller one increases the force, another perspective argues that the net force remains the same. The challenge lies in accurately determining the center of charge for each configuration in three-dimensional space. Ultimately, the conversation highlights the complexities of calculating electrostatic forces in different arrangements.
oronanschel
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given to solid half charged sphere Insulators.

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

KNSdL.jpg
 
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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.
 
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
 
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?
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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