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  4. Three identical charges are placed at the comers of an equilateral triangle. If the force between any two charges is F, then the net force on each will be

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Q. Three identical charges are placed at the comers of an equilateral triangle. If the force between any two charges is F, then the net force on each will be

CMC MedicalCMC Medical 2007

Solution:

Net force on each charge will be $ {{F}_{net}}=\sqrt{{{F}^{2}}+{{F}^{2}}+2{{F}^{2}}\cos 60{}^\circ } $ $ \Rightarrow $ $ {{F}_{net}}=\sqrt{2{{F}^{2}}+2{{F}^{2}}\times \frac{1}{2}} $ $ \Rightarrow $ $ {{F}_{net}}=\sqrt{2{{F}^{2}}+{{F}^{2}}} $ $ \Rightarrow $ $ {{F}_{net}}=\sqrt{3{{F}^{2}}} $ $ \therefore $ $ {{F}_{net}}=\sqrt{3}F $