Two point charges `Q and -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.

Options

A. at `x = r//3` only
B. at `x = -r//5` only
C. both at `x = r//3` and at `x = -r//5`
D. there exist two points on the axis where the electric field is zero.

Answer

c

Explanation

`(k Q)/(4 x_1) = (k Q)/(r + x_1)` or `r + x_1 = 4 x_1` or `x_1 = r //3`
or `(k Q)/(4 x_2) = (k Q)/(r - x_2)` or `x_2 = ( r)/(5)`.
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