What is the net force on the -1nC charge in this Coulomb's Law problem?

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SUMMARY

The net force on the -1nC charge in the given Coulomb's Law problem is calculated using Coulomb's Law and trigonometric equations. The force between the two known charges is determined to be 1.44x10^-4 N, with a downward component calculated as 1.25x10^-4 N. The error in the initial calculation arises from misunderstanding that the net force must account for the contributions from both known charges acting on the -1nC charge. The correct approach involves summing the forces from both charges to find the total net force.

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Lilian Chan
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Homework Statement


link: https://ibb.co/Xy9s6DR
What is the magnitude of this force?

Homework Equations


Coulomb's Law
Trig equations

The Attempt at a Solution


(.05 m)xcos(60)=0.025m (the distance between the two known charges)
F(between the two known charges)=(9x20^9)(1x10^-9)(10x10^-9)/(0.025)^2=1.44x10^-4
F(that points down)=sin(60)*1.44x10^-4=1.25x10^-4N

The homework system says I got it wrong but I'm not seeing where.
 

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Lilian Chan said:
(9x20^9)
9x10^9
Lilian Chan said:
F(between the two known charges)
That's only the force between those two charges. The F in the diagram is the net force on the -1nC charge from the other two.
 
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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