Single Choice

Calculate the electric potential at the center of the square :

A0
B$$k\dfrac{2q}{s^2}$$
C$$k\dfrac{4q}{s^2}$$
D$$k\dfrac{(4\sqrt{2})q}{s}$$
Correct Answer

Solution

Let the distance between each corner and the center of square be $$x$$.
$$\therefore$$ $$s^2 =x^2 + x^2 $$ $$\implies x = \dfrac{s}{\sqrt{2}}$$
Potential at the center due to charge at corner 1, $$V_1 = \dfrac{k q}{x} = \dfrac{\sqrt{2}kq}{s}$$
The square is symmetric about its center.
Thus total potential at the center $$V =4V_1 = k\dfrac{4\sqrt{2} q}{s}$$

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