Question

Point charges of $3\times {10}^{-9}C$ are situated at each of the three corners of a square whose side is $15cm$. The magnitude and direction of electric field at the vacant corner of the square is :

• A. $2294V/m$ along the diagonal
• B. $9622$ V/m along the diagonal
• C. $22.0V/m$ along the diagonal
• D. zero

Answer 1

The correct option is A $2294V/m$ along the diagonal

Effective electric field will be $\sqrt{2}{E}_1+E_2$ along the diagonal.
$\Rightarrow E=\frac{k{q}_1}{(15\times {10}^{-2}{)}^2}\sqrt{2}+\frac{k{q}_1}{(\sqrt{2}\times 15\times {10}^{-2}{)}^2}$

$=\frac{9\times {10}^9\times 3\times {10}^{-9}\times \sqrt{2}}{225\times {10}^{-4}}+\frac{9\times {10}^{-9}\times 3\times {10}^{-9}}{2\times 225\times {10}^{-4}}$

$=\frac{38.1}{225\times {10}^{-4}}+\frac{13.5}{225\times {10}^{-4}}$

$=\frac{51.6}{225\times {10}^{-4}}$

$E=2293.33V/m$
$=2294V/m$