InterviewSolution
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InterviewSolution
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consider three charges q_(1),q_(2),q_(3)eachequal to q at the vertices of anequilateral triangleof side l what is the force on acharge Qplaced at the centroidof the triangle |
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Answer» Solution :In thegiven EQUILATERAL triangle ABCof sides of length l if we draw a perpendicualre ADto the side BC AD=AC cos `30^(@) =SQRT(3)//2` l and the distanceAO of the CENTROID o from A is `(2/3)` AD=`(1/sqrt(3))` l by symmatry AO=BO=CO force `F_(1)` and Q due to chargeq at A=`(3)/(4piepsilon_(0))(Qq)/(l^(2))` along AO force `F_(2)` and Q due to chargeq at B=`(3)/(4piepsilon_(0))(Qq)/(l^(2))` along AO force `F_(3)` and Q due to chargeq at C=`(3)/(4piepsilon_(0))(Qq)/(l^(2))` along AO parallelogram LAW thereforethe toal force on Q =`(3)/(4piepsilon_(0))(Qq)/(4piepsilon_(0))(Qq)/(l^(2))(vecr-vecr)` =0 where `vecr` isthe unit vectoralong OA it is clear alos by symmetry that the three forces will SUM to zero considerwhat wouldhappen if the system was rotated through `60^(@)`about O |
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