Four point charges are placed at the corners of a square with diagonal 2a as shown. What is the total electric field at the center of the square?

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kq/a² at an angle 45⁰ above the +x-axis

kq/a² at an angle 45^o below the -x-axis

3kq/a² at an angle 45^o above the -x-axis

3kq/a² at an angle 45^o below the +x-axis

answer is B.

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Detailed Solution

At center electric field due to both 3q will be canceled. Now net field at center is

$\begin{array}{l} E = E_{1} - E_{2} = \frac{k 2 q}{(a)^{2}} - \frac{k q}{(a)^{2}} = \frac{k q}{(a)^{2}} \\ This is 45^{\circ} below negative x -axis. \end{array}$

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