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https://texercises.com/exercise/forces-between-three-point-charges-2d/
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Exercise:
Three charges Q_ Q_ and Q_ are placed at the corners of an equilateral triangle. vecF_ and vecF_ are the resultant forces acting on the first two charges. Determine the resultant force acting on Q_. center includegraphicswidth.textwidth#image_path:threcharges-d# center

Solution:
The resultant force on the closed system of the three charges has to be zero i.e. vecF_+vecF_+vecF_vec It follows for vecF_: vecF_-leftvecF_+vecF_right The force on Q_ corresponds to the negative vector of the other two forces.
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Exercise:
Three charges Q_ Q_ and Q_ are placed at the corners of an equilateral triangle. vecF_ and vecF_ are the resultant forces acting on the first two charges. Determine the resultant force acting on Q_. center includegraphicswidth.textwidth#image_path:threcharges-d# center

Solution:
The resultant force on the closed system of the three charges has to be zero i.e. vecF_+vecF_+vecF_vec It follows for vecF_: vecF_-leftvecF_+vecF_right The force on Q_ corresponds to the negative vector of the other two forces.
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Tags
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Difficulty
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