Question

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?

Answer 1

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

Where,
(Sides) AB = BC = CD = AD = 10 cm
(Diagonals) AC = BD = $10\sqrt 2$ cm
AO = OC = DO = OB = $5\sqrt 2$ 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.