Three point charges +2micro coulomb, -3micro coulomb and -3micro coulomb are kept at the vertices A, B and C respectively of an equilateral triangle. What should be the sign and magnitude of the charge to be placed at the mid point of side BC so that the charge at A is in in equilibrium? Each side of the triangle is 20cm.



The charge to be placed is +2.25 microcoulombs
the resultant due to -3 microcoulombs at B and C
is k(-3 microcoulombs)/r²
where r is the distance of A from B and C
so to be in equilibrium a force  k(3 microcoulombs)/r² should act on charge at A
so the charge at midpoint is Q
kQ/(10√3)²=k(+3 microcoulombs)/(20)²
Q=+3 microcoulombs(3/4)=+2.25  microcoulombs