Question

The three charges q/2, q and q/2 are placed at the corners A , B and C of a square of side ‘ a ’ as shown in figure. The magnitude of electric field (E) at the corner D of the square is

Fig.

• A. $\frac{q}{4π∈_0a_2} ( \frac{1}{\sqrt2} + \frac{1}{2})$
• B. $\frac{q}{4π∈_0a_2} ( 1 + \frac{1}{\sqrt2} )$
• C. $\frac{q}{4π∈_0a_2} ( 1 - \frac{1}{\sqrt2} )$
• D. $\frac{q}{4π∈_0a_2} ( \frac{1}{\sqrt2} - \frac{1}{2} )$

Answer 1

Answer: (A)

$\frac{q}{4π∈_0a_2} ( \frac{1}{\sqrt2} + \frac{1}{2})$

Answer 2

The correct answer is (A) : $\frac{q}{4π∈_0a_2} ( \frac{1}{\sqrt2} + \frac{1}{2})$
$| E_0 | = \frac{kq/2}{a²} \sqrt2 + \frac{kq}{( a\sqrt2 )²}$
$= \frac{kq}{\sqrt2a²} + \frac{kq}{2a²}$
$=\frac{kq}{a²} ( \frac{1}{\sqrt2} + \frac{1}{2} ), k = \frac{1}{4π∈_0}$