Question

Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the charge placed at the centre is (each side of triangle is l)

Answer 1

Answer:

the electrostatic force on the charge placed at the centre is ZERO

Explanation:

Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the charge placed at the centre is (each side of triangle is l)

Let say ABC is triangle and O is center

Let say BC is Base on X axis  & AB * AC are above X - AXIS

BC = AB = AC = l

BO = CO = AO = l/√3

Charges Placed at a b * c are q

charge place on center = 1

Force by Charge B on Charge O is repulsive force at an angle 30° with X axis  

F = q * 1 /(l/√3)²  = 3ql

Force along x axis = 3qlcos30° = 3√3ql/2

Force along y axis = 3qlSin30° = 3ql/2

Force by Charge C on Charge O is repulsive force at an angle 150° with X axis  

F = q * 1 /(l/√3)²  = 3ql

Force along x axis = 3qlcos150° = -3√3ql/2

Force along y axis = 3qlSin150° = 3ql/2

Force by Charge A on Charge O is repulsive force at an angle 270° (or - 90°) with X axis  

F = q * 1 /(l/√3)²  = 3ql

Force along x axis = 3qlcos(-90°) = 0

Force along y axis = 3qlSin(-90°) = -3ql

Sum of all forces along x -axis = 3√3ql/2  -3√3ql/2 + 0 = 0

Sum of all forces along y -axis = 3ql/2 + 3√3ql/2 - 3ql = 0

Hence net Force = 0

the electrostatic force on the charge placed at the centre is ZERO