Electrostatics Question 672

Question: It is required to hold equal charges $ q $ in equilibrium at the comers of a square. What charge when placed at the center of the square will do this?

Options:

A) $ -\frac{q}{2}(1+2\sqrt{2}) $

B) $ \frac{q}{2}(1+2\sqrt{2}) $

C) $ \frac{q}{4}(1+2\sqrt{2}) $

D) $ -\frac{q}{4}(1+2\sqrt{2}) $

Show Answer

Answer:

Correct Answer: D

Solution:

[d] $ AC=\sqrt{2l}=BD $ or $ BO=\frac{1}{\sqrt{2}} $

$ F _{BO}=F _{BD}+(F _{BA}+F _{BC})cos45{}^\circ $

Solving, we get $ Q=\frac{q}{4}(1+2\sqrt{2}) $ and Q should be negative of q.



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