Question

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

Options

• 8L

• 4L

• 2L

• L

Answer 1

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

Explanation:

Let P is the observation point at a distance r from -2q and at (L+r) from +8q.

Given Now, Net EFI at P = 0

`therefore vec"E"_1` = EFI (Electric Field Intensity) at P due to +8q

`vec"E"_2` = EFI (Electric Field Intensity) at P due to -2q

`abs(vec"E"_1) = abs(vec"E"_2)`

`therefore ("k" (8"q"))/("L + r")^2 = ("k" (2 "q"))/"r"^2`

`therefore 4/("L + r")^2 = 1/("r")^2`

`4"r"^2 = ("L + r")^2`

`2"r" = "L + r"`

r = L

`therefore` P is at x = L + L = 2L from origin

`therefore` Correct Option is (iii) 2L