Four point charges `q_(A) = 2 mu C , q_(B) = -5 mu C, q_(C) = 2 mu C and q_(D) = -5 mu C` are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of `1 mu C` placed at the center of the square ?

Options

A. `0 N`
B. `1 N`
C. `2 N`
D. `3 N`

Answer

A

Explanation

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 = `5sqrt(2) cm`
A charge of amount `1muC` 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 `1muC` charge at centre O is zero.