Two point charge `+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

Suppose that at point B, net electric field is zero due to charges `8q and -2q`.
`vecE_(BO)=(-1)/(4 pi e_0) . (8q)/a^2 hat I vecE_(BA)=1/(4 pi e_0) (+2q)/(a+L)^2 hat i`
According to condition `vecE_(BO)+vecE_(BA)=0`
`implies 1/(4 pi e_0) (8q)/a^2= 1/(4 pi e_0) (2q)/(a+L)^2 or 2/a=1/(a+L) or 2a+2L=a or 2L=-a`
Thus, at distance 2L from origin, net electric field will be zero.