Question

A point charge q is fixed at each of the two opposite corners of a square. A third point charge Q is placed at each of the other two corners. If one of the charge Q experiences no force,then

• A. $Q=\sqrt{2}q$
• B. $Q=-2\sqrt{2}q$
• C. $Q=\sqrt{2}{q}^2$
• D. $Q=-2\sqrt{2}{q}^2$

Answer 1

The correct option is B $Q=-2\sqrt{2}q$


If the charge at B experiences zero net force, then
$F_{AB}cos45+F_{CB}cos45+F_{DB}=0$
$\frac{1}{4\pi {ϵ}_0}[\frac{qQ}{a^2}\frac{1}{\sqrt{2}}+\frac{qQ}{a^2}\frac{1}{\sqrt{2}}+\frac{QQ}{(a\sqrt{2}{)}^2}]=0$
$\frac{\sqrt{2}qQ}{a^2}=-\frac{QQ}{2a^2}\Rightarrow Q=-2\sqrt{2}q$