Question

Point charges $q$ , $-q$ , $2Q$ and $Q$ are placed in order at the corners $A$ , $B$ , $C$ and $D$ of a square of side $2b$ . If the field at the midpoint of $CD$ is zero, then $\frac{q}{Q}$ is

• A. $1$
• B. $2$
• C. $\frac{2 \sqrt{2}}{5}$
• D. $\frac{5 \sqrt{5}}{2}$

Answer 1

Answer: (D)

$E=E_{C}-E_{D}-E_{A}cos \theta -E_{B}cos⁡\theta $
$\frac{k \left(2 Q\right)}{b^{2}}-\frac{k Q}{b^{2}}=2\times \frac{k q b}{\left(b^{2} + 4 b^{2}\right)^{\frac{3}{2}}}$
$\Rightarrow Q=\frac{2 q}{5 \sqrt{5}}$