Consider 3 charges q1 q2 q3 equals to 15 micro columbs ,10 micro columbs, 15 micro columbs are at vertices of the triangle of lenght 2cms.What is the force on a charge 10 micro columbs placed at the centroid of triangle
Answers
The question should have been:
Consider three charges q1, q2, q3 each equal to q at the vertices of an equilateral triangle of side l. What is the force on the charge Q placed at the centroid of the triangle ?
In a equilateral triangle, all sides are equal and is 600. Similarly, all sides are equal and let it be L.
In the figure, from ∆ BOD, Angle OBD = 30° and BD = L/2
AD = AC cos 300 = AC (√3/2) = L (√3/2)
For a centroid, AO from the point A = 2/3 of AD as the centroid divides the line in the ratio 2:1
Hence, 2/3 AD = (2/3) L (√3/2)
= L (1 / √3)
Force F1 on Q due to charge q at A is
= (1/4∏є0 ) * Qq/(L2/3) = (3/4∏є0 ) * Qq / L2 along AO
Force F2 on Q due to charge q at B is
= (1/4∏є0 ) * Qq/(L2/3) = (3/4∏є0 ) * Qq / L2 along BO
Force F3 on Q due to charge q at C is
= (1/4∏є0 ) * Qq/(L2/3) = (3/4∏є0 ) * Qq / L2 along CO
Resultant of force F2 and force F3 by vector parallelogram of addition is
= (3/4∏є0 ) * Qq / L2 along OA
Total force on Q due to F1 and the resultant of the force F2 and F3 is
= (3/4∏є0 ) * Qq / L2 along AO + (3/4∏є0 ) * Qq / L2 along OA
= 0 as vector magnitude is same and direction is opposite
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