Two point charge `-q` and `+q//2` are situated at the origin and the point `(a,0,0)` respectively. The point along the `X`-axis where the electic field Vanishes is

Options

A. `x=(a)/(sqrt(2))`
B. `x=sqrt(2)a`
C. `x=(sqrt(2)a)/(sqrt(2)-1)`
D. `x=(sqrt(2)a)/(sqrt(2)+1)`

Answer

c

Explanation

Suppose the field vanishes at a (distance `x`), we have
`(kq)/(x^(2))= (kq//2)/((x-a)^(2))` or `2(x-a)^(2)=x^(2)`
or `sqrt(2)(x-a)=x`
or `(sqrt(2)-1)x= sqrt(2)a` or `x=((sqrt(2)a)/(sqrt(2)-1))`