Question

The three charges $\frac{q}{2},q$ and $\frac{q}{2}$ are placed at the corners $A,B$ and $C$ of a square of side $‘a^{\prime }$ as shown in figure. The magnitude of electric field $\left(E\right)$ at the corner $D$ of the square is

• A. $\frac{q}{4\pi {\epsilon }_0{a}^2}(\frac{1}{\sqrt{2}}-\frac{1}{2})$
• B. $\frac{q}{4\pi {\epsilon }_0{a}^2}(1+\frac{1}{\sqrt{2}})$
• C. $\frac{q}{4\pi {\epsilon }_0{a}^2}(1-\frac{1}{\sqrt{2}})$
• D. $\frac{q}{4\pi {\epsilon }_0{a}^2}(\frac{1}{\sqrt{2}}+\frac{1}{2})$

Answer 1

The correct option is D $\frac{q}{4\pi {\epsilon }_0{a}^2}(\frac{1}{\sqrt{2}}+\frac{1}{2})$

$|E_0|=\frac{\frac{kq}{2}}{a^2}\sqrt{2}+\frac{kq}{(a\sqrt{2}{)}^2}$

$=\frac{kq}{2}\sqrt{2}{a}^2+\frac{kq}{2a^2}$

$=\frac{kq}{a^2}(\frac{1}{\sqrt{2}}+\frac{1}{2}),k=\frac{1}{4\pi {\epsilon }_0}$

$\Rightarrow$ Option A is correct.