A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then the Q/q equals
Answer & explanation
Correct answer: option 1
$ \text{ Force on Q due to charge q is } F_1 = \frac{kqQ}{a^2}$
$\text { a is length of side of square }$
$ \text{Force due to charges q on Q are perpendicular so resultant of two are }$
$F_{1R} = \frac{kqQ\sqrt 2}{a^2}$
$\text{Force due to charge Q } F_2 = \frac{KQ^2}{2a^2} $
$\text{Since resultant force is zero } F_{net} = 0$
$ \Rightarrow \frac{kqQ\sqrt 2}{a^2} + \frac{KQ^2}{2a^2} =0$
$\Rightarrow q = -\frac{Q}{2\sqrt 2}$
$\Rightarrow \frac{Q}{q} = -2\sqrt 2$