Four point charges qA = 2 µC, qB = −5 µC, qC = 2 µC, and qD = −5 µC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?

Question 1.6: Four point charges q_A = 2 µC, q_B = −5 µC, q_C = 2 µC, and q_D = −5 µC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?

Method - 1

Answer:

The given figure shows a square of side 10 cm with four charges placed at its corners. O is the centre of the square.

(Sides) AB = BC = CD = AD = 10 cm
(Diagonals) AC = BD = cm
AO = OC = DO = OB = cm
A charge of amount 1μC is placed at point O.
Force of repulsion between charges placed at corner A and centre O is equal in
magnitude but opposite in direction relative to the force of repulsion between the
charges placed at corner C and centre O. Hence, they will cancel each other.
Similarly, force of attraction between charges placed at corner B and centre O is
equal in magnitude but opposite in direction relative to the force of attraction
between the charges placed at corner D and centre O. Hence, they will also cancel
each other. Therefore, net force caused by the four charges placed at the corner of
the square on 1 μC charge at centre O is zero.

Method - 2