Question

Three charges each of $+4\mu C$, are placed at the corner $B,C,D$ of square $ABCD$ of side $1m$. The electric field at the center $O$ of the square is

• A. $7.2\times {10}^{4}N$ towards $A$
• B. $7.2\times {10}^{4}N$ towards $C$
• C. $3.6\times {10}^{4}N$ towards $A$
• D. $3.6\times {10}^{4}N$ towards $C$

Answer 1

The correct option is A $7.2\times {10}^{4}N$ towards $A$

$\overrightarrow{E}$ due to $B$ and $C$ are equal in magnitude and opposite direction.

Therefore, ${\overrightarrow{E}}_{net}={\overrightarrow{E}}_{duetoD}$

$E_D=\frac{k\times (4\times {10}^{-6})}{r^2}$

$r=OD=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$

$\therefore E_D=8k\times {10}^{-6}$

$=E_D=7.2\times {10}^{4}N/C$ towards $A$