Electrostatic force between to spheres

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SUMMARY

The discussion centers on the electrostatic force between two solid half-charged spheres, specifically analyzing the differences in force when arranged in two configurations, A and B. According to Coulomb's law, the force is influenced by the distance between the centers of charge, which is shorter in configuration B due to the flipping of the larger half-sphere. Participants debate the validity of the claim that the net force remains the same, with a consensus that configuration B results in a greater force due to the closer proximity of the centers of charge.

PREREQUISITES
  • Coulomb's Law
  • Understanding of electrostatic forces
  • Concept of center of charge
  • Basic geometry in three-dimensional space
NEXT STEPS
  • Study the implications of Coulomb's Law in three-dimensional configurations
  • Research the concept of electric field shapes for charged objects
  • Explore the calculation of forces between non-point charges
  • Investigate the behavior of electric fields in insulators
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Physics students, electrical engineers, and anyone interested in electrostatics and the behavior of charged objects in different configurations.

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 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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