चार बिंदु आवेश $q_{ A }=2 \mu C , q_{ B }=-5 \mu C , q_{ C }=2 \mu C$ तथा $q_{ D }=-5 \mu C , 10 cm$ भुजा के किसी वर्ग $ABCD$ के शीर्षों पर अवस्थित हैं। वर्ग के केंद्र पर रखे $1 \mu C$ आवेश पर लगने वाला बल कितना है?

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 $1 \,\mu\, C$ 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 comer $B$ 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 $1 \,\mu\, C$ charge at centre $O$ is zero.