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Two point charges $Q a n d - Q / 4$ placed along the x-axis are separated by a distance r. Take $- Q / 4$ as origin and it is placed at the right of Q. Then the potential is zero.

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at $x = - r / 5 o n l y$

there exist two points on the axis where the electric field is zero

at x = r/3 only

both at $x = r / 3 a n d x = - r / 5$

answer is C.

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Detailed Solution

$\frac{k Q}{4 x_{1}} = \frac{k Q}{r + x_{1}} o r r + x_{1} = 4 x_{1} o r x_{1} = \frac{r}{3}$

or $\frac{k Q}{4 x_{2}} = \frac{k Q}{r - x_{2}} o r x_{2} = \frac{r}{5}$

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