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Two point charges +8q and -2q are locate...

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

A

`2L`

B

`L/4`

C

`8L`

D

`4L`

Text Solution

Verified by Experts

The correct Answer is:
A
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.
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