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Question Number 133394 by Dwaipayan Shikari last updated on 21/Feb/21

Commented by Dwaipayan Shikari last updated on 21/Feb/21

$$Threeindenticalpointcharges,eachofmass\mathit{m}andcharge$$$$\mathit{Q},hangingfromthreestrings.Findthevalueof\mathit{Q}interms$$$$of\mathit{m},\mathit{L}and\mathit{\theta }\left(Theyareinequilibrium\right)$$

Commented by Dwaipayan Shikari last updated on 21/Feb/21

$$Electrostaticforceactingonchargewhichisonleft$$$$=\frac{Q^2}{4\pi {ϵ}_0{L}^2{sin}^2\theta }+\frac{Q^2}{4\pi {ϵ}_0{\left(2Lsin\theta \right)}^2}=\frac{5Q^2}{16\pi {ϵ}_0{L}^2{sin}^2\theta }$$$$Tension=T$$$$Tcos\theta =mg\Rightarrow T=\frac{mg}{cos\theta }$$$$Tsin\theta =\frac{5Q^2}{16\pi {ϵ}_0{L}^2{sin}^2\theta }\Rightarrow \frac{16\pi {ϵ}_0}{5}{mgL}^{2}tan\theta {sin}^2\theta =Q^2$$$$\Rightarrow Q=4Lsin\theta \sqrt{\frac{\pi {ϵ}_0}{5}mgtan\theta }$$

Commented by Dwaipayan Shikari last updated on 22/Feb/21

$$Isittrue?$$

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