Two point charges`(+Q)` and `(-2Q)` are fixed on the `X`-axis at position `a` and `2a` from origin respectively. At what position on the axis, the resultant electric field is zero

Options

A. Only `x= sqrt(2)a`
B. Only `x= -sqrt(2)a`
C. Both `x= +-sqrt(2)a`
D. `x=(3a)/(2)cm`

Answer

b

Explanation

Suppose electric field is zero at a point `P` lies at a distance `d` from the charge `+Q`.
At `P(kQ)/(d^(2))=(k(2Q))/((a+d)^(2))`
`implies (1)/(d^(2))= (2)/((a+d)^(2))implies d= (a)/((sqrt(2)-1))`

Since `dgta` i.e., point `P` must lies on negative `x`-axis as shown at a distance `x` from origin hence `x= d-a`
`=(a)/((sqrt(2)-1))= a= sqrt(2)a`. Actually `P` lies on negative `x`-axis so `x= -sqrt(2)a`