Question

What will be the magnitude of electric field at point $O$ as shown in figure?
Each side of the figure is $\mid$ and perpendicular to each other?

• A. $\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{l^{2}}$
• B. $\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{\left(2 l^{2}\right)}(2 \sqrt{2}-1)$
• C. $\frac{q}{4 \pi \varepsilon_{0}(2 l)^{2}}$
• D. $\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{2 l^{2}}(\sqrt{2})$

Answer 1

Answer: (B)

$E_{1}=\frac{k q}{l^{2}}=E_{2}$
$E_{3}=\frac{k q}{(\sqrt{2} l)^{2}}=\frac{k q}{2 l^{2}}$
$E=\frac{\sqrt{2} k q}{l^{2}}-\frac{k q}{2 l^{2}}$
$=\frac{k q}{2 l^{2}}(2 \sqrt{2}-1)$