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Q.

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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a

$\frac{q}{4 π ϵ_{0} a^{2}} (\frac{1}{\sqrt{2}} + \frac{1}{2})$

b

$\frac{q}{4 π ϵ_{0} a^{2}} (\frac{1}{\sqrt{2}} - \frac{1}{2})$

c

$\frac{q}{4 π ϵ_{0} a^{2}} (1 - \frac{1}{\sqrt{2}})$

d

$\frac{q}{4 π \in_{0} a^{2}} (1 + \frac{1}{\sqrt{2}})$

answer is A.

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Detailed Solution

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$\begin{array}{l} {(E_{net})}_{D} = \frac{k q}{2 a^{2}} + \frac{\sqrt{2} k q}{2 a^{2}} \\ {(E_{net})}_{D} = \frac{k q}{a^{2}} (\frac{1}{2} + \frac{1}{\sqrt{2}}) \\ {(E_{net})}_{D} = \frac{q}{4 π ϵ_{0} a^{2}} (\frac{1}{2} + \frac{1}{\sqrt{2}}) \end{array}$

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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 :