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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 figure ? |
Answer» Solution :SITUATION given in the statement is depicted in following figure.  Here O is the centroid of an equilateral triangle `TRIANGLEABC` . Hence, OA = OB = OC = r ... (1) Electric repulsive forces exerted by `q_(1),q_(2), q_(3)`on `q_(4)` have same magnitudes each EQUAL to F because, `F_(41) = F_(42) = F_(43) =F = k(QQ)/r^(2)`......(2) Suppose, `vecF^(.) = vecF_(42) + vecF_(43)` `therefore F. = sqrt(F^(2) + F^(2) + 2F F cos (120^(@))` `(therefore F_(42) = F_(43) = F)` `=sqrt(2F^(2) + 2F^(2) (-1/2))` (`therefore` Angle between `vecF_(42)` and `vecF_(43)` is `theta = 120^(@)`) `=sqrt(F^(2))` =F.............(3) If resultant force exerted on `q_(4) =Q` is `vecF_(4)` then `vecF_(4) = vecF_(41) + vecF_(42) + vecF_(43)` `=vecF_(41) + vecF^(.)` `=F(-hatj) + F(hatj)` `therefore vecF_(4)=vec0` |
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