Charges Q are placed at the ends of a diagona | vedclass

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Question

(A) Let the side of the square be $a$. Consider a charge $Q$ at corner $D$. The other charges are at $A$ (charge $q$),$B$ (charge $Q$),and $C$ (charge

Vedclass · Accepted Answer

$Q = -2 \sqrt{2} q$,$q$ being negative

Vedclass · Answer

(A) Let the side of the square be $a$. Consider a charge $Q$ at corner $D$. The other charges are at $A$ (charge $q$),$B$ (charge $Q$),and $C$ (charge $q$).The force on $Q$ at $D$ due to $q$ at $A$ is $F_A = \frac{K Q q}{a^2}$ (along $DA$).The force on $Q$ at $D$ due to $q$ at $C$ is $F_C = \frac{K Q q}{a^2}$ (along $DC$).The resultant of these two forces is $F_{AC} = \sqrt{F_A^2 + F_C^2} = \sqrt{2} \frac{K Q q}{a^2}$ (along the diagonal $DB$).The force on $Q$ at $D$ due to $Q$ at $B$ is $F_B = \frac{K Q^2}{(\sqrt{2} a)^2} = \frac{K Q^2}{2 a^2}$ (along the diagonal $DB$).For the net force on $Q$ to be zero,the sum of these forces must be zero:$\frac{K Q^2}{2 a^2} + \sqrt{2} \frac{K Q q}{a^2} = 0$Dividing by $\frac{K Q}{a^2}$ (assuming $Q 
eq 0$):$\frac{Q}{2} + \sqrt{2} q = 0$$Q = -2 \sqrt{2} q$Since $Q$ and $q$ must have opposite signs to balance,if $Q$ is positive,$q$ must be negative.

Charges $Q$ are placed at the ends of a diagonal of a square and charges $q$ are placed at the other two corners. The condition for the net electric force on $Q$ to be zero is

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