Question

Two point charges $- q$ and $\frac{ q }{2}$ are situated at the origin and at the point $( a , 0,0)$ respectively. The point along the x-axis where the electric field vanishes is

• A. $x=\frac{a}{\sqrt{2}}$
• B. $x=\sqrt{2}$ a
• C. $x=\frac{\sqrt{2} a}{\sqrt{2}-1}$
• D. $x=\frac{\sqrt{2} a}{\sqrt{2}+1}$

Answer 1

Answer: (C)

Suppose the field vanishes at a distance $x$ we have
$\frac{ Kq }{ x ^{2}}=\frac{ Kq / 2}{( x - a )^{2}}$
$2( x - a )^{2}= x ^{2}$
$\sqrt{2}( x - a )= x$
$\sqrt{2} x-\sqrt{2} a=x$
$\sqrt{2} x-x=\sqrt{2} a$
$x=\frac{\sqrt{2} a}{\sqrt{2}-1}$