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Consider three charges q_(1), q_(2), q_(3) each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle, as shown in Fig. ? |
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Answer» Solution :Letthe force actingon +Q chargeat O dueto +q at A be `F_(1)`, +q at B be `F_(2)` and -q at C be `F_(3)` Here `AO=BO=CO=(d)/(sqrt(3))`  In magnitude `F_(1)=F_(2)=F_(3)=(1)/(4pi in_(0))(3q^(2))/(d^(2))` RESULTANT of `F_(1) and F_(2)` is `F_(4)=(1)/(4pi in_(0)) (3q^(2))/(d^(2))` (as angle between `F_(1) and F_(2)` is `120^(0)`) Directionof `F_(4)` is ALONGTHE direction of `F_(3)`. Hence the resultantforce on +q at O is `F=F_(3)+F_(4)=(3q^(2))/(2pi in_(0)d^(2))` |
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