No idea on how to do this problem

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To achieve a net vertical force on the charge at corner A, the horizontal forces from the charges at the other corners must cancel each other out. This requires placing a charge at the empty corner that creates a force equal in magnitude but opposite in direction to the horizontal forces exerted by the +3μC charges. The appropriate charge should be negative to counteract the positive charges. The calculation involves using Coulomb's law to determine the necessary magnitude and sign of the charge. Understanding these force interactions is crucial for solving the problem effectively.
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Q: In the rectangle in the drawing, a charge is to be placed at the empty corner to make the net force on the charge at corner A point along the vertical direction. What charge (magnitude and algebraic sign) must be placed at the empty corner?

The picture shows a normal rectangle. The upper left and lower left corners have a sphere with a charge of +3μC, and the lower right corner has a sphere with a charge of +3μC. The upper right corner is the blank one and point A is located at the lower left sphere. The upper horizontal side/line shows a length of 4d, and the right vertical side/line shows d. I know you have to use f = k(q1)(q2) / r^2 , but I don't know where to go from there.

Help is greatly appreciated!
 
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welcome to pf!

hi dowz0r! welcome to pf! :smile:
dowz0r said:
… a charge is to be placed at the empty corner to make the net force on the charge at corner A point along the vertical direction.

if the net force is vertical, then you need the horizontal components of the forces to add to zero :wink:
 
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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