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Q.

Four charges of + q, – q, +q and +q are placed at the corners A, B, C and D of a square. Find the resultant force on charge at D.

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a

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

b

$\frac{2 q^{2}}{{πε}_{0} a^{2}}$

c

$\frac{q^{2}}{8 {πε}_{0} a^{2}} 2 \sqrt{2}$

d

zero

answer is A.

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Detailed Solution

$Net = \sqrt{2} F - \frac{F}{2}$
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$= F (\sqrt{2} - \frac{1}{2}) = \frac{1}{4 {πε}_{0}} \frac{q^{2}}{a^{2}} (\sqrt{2} - 1 / 2)$

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Four charges of + q, – q, +q and +q are placed at the corners A, B, C and D of a square. Find the resultant force on charge at D.