The three charges q/2, q and q/2 are placed at the corners A, B and C… | JEE Main 2022 (28 Jun, Shift 1)

Q25JEE Main 2022 · 28 JUN · SHIFT 1Medium

Electric Field & Field Lines

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:

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Answer: (a)

Let $E_0 = \dfrac{q}{4\pi\varepsilon_0 a^2}$ . $A$ and $C$ ( $q/2$ each, distance $a$ ) give $\dfrac{E_0}{2}$ each, at right angles.
Their resultant along diagonal $BD$ : $\sqrt{2}\cdot\dfrac{E_0}{2} = \dfrac{E_0}{\sqrt{2}}$
$B$ ( $q$ , distance $\sqrt{2}a$ ) gives $\dfrac{E_0}{2}$ , also along $BD$ away from $B$ .
$E = E_0\left(\dfrac{1}{\sqrt{2}} + \dfrac{1}{2}\right)$
So the answer is (a).

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