Three charges, each of $+4 \mu \mathrm{C}$, are placed at the corners $A, B, C$ of a square $A B C D$ of side 1 m . What is the magnitude (in $\mathrm{NC}^{-1}$ ) of electric field at point $O$ towards point $D ?$

• A

  66000
• Correct answer
  B

  72000
• C

  51000
• D

  64000

Solution

$E_{\mathrm{A}}$ cancels $E_{\mathrm{C}}$. At $\begin{aligned} O ; E_B & =\frac{1}{4 \pi \varepsilon_0} \frac{q}{\left(\frac{d}{\sqrt{2}}\right)^2} \\ & =\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{d^2} \\ & =\frac{9 \times 10^9 \times 2 \times 4 \times 10^{-6}}{1^2} \\ & =72 \times 10^4 \mathrm{~N} / \mathrm{C}, \text { towards } D \\ & =72000 \mathrm{~N} / \mathrm{C}\end{aligned}$

Hence, the correct answer is option: 'B'.