Question

Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is

(1) \(\frac {(1 + \sqrt {3})}{r}\)

(2) \(\frac {r}{3 (1 + \sqrt {3})}\)

(3) \(\frac {r}{(1+\sqrt {3})}\)

(4) \(r (1 +\sqrt {3})\)

Answer 1

(3) \(\frac {r}{(1+\sqrt {3})}\)

\((\vec{E}_{net})_p =0\)

\(\frac {kq}{x^2}= \frac {k.3q}{(r-x)^2}\)

\((r-x)^2 = 3 x^2\)

\(r-x =\sqrt {3}x\)

\(x = \frac {r}{\sqrt {3}+1}\)