Two point charges `+8q` and `-2q` are located at `x=0` and `x=L` respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is

Options

A. `2L`
B. `L//4`
C. `8L`
D. `4L`

Answer

A

Explanation

Let the net electric field due to two given charges be zero at `P`, where `Op = x`.

for the electric field to be zero
`:. E_(AP) = B_(BP) = (K 8 q)/(x^(2)) = (K(2q))/((x- L)^(2))`
`(4)/(x^(2)) = (1)/(x-L)^(2))` or `(2)/(x) = (1)/(x-L)`
or `2x - 2L = x` or `x = 2L`