Four points charges -q,+q,+q and -q are placed on y-axis at y=-2d, y=-d,y=+d and y=+2d, respectively. The magnitude of the electric field E at a point on the x-axis at x=D, with `Dgtgtd`, will behave as :

Options

A. `E prop 1/D^4`
B. `E prop 1/D`
C. `E prop 1/D^2`
D. `E prop 1/D^3`

Answer

A

Explanation

Electric field at `p=2E_(1)costheta_(1)-2E_(1)costheta_(2)`

`=(2Kq)/((d^(2)+D^(2)))xx(D)/((d^(2)+D^(2))^(1//2))-(2Kq)/([(2d)^(2)+D^(2)])xx(D)/([(2d)^(2)+D^(2)]^(1//2))`
`2KqD[(d^(2)+D^(2))^(-3//2)-(4d^(2)+D^(2))^(-3//2)]=(2KqD)/(D_3)[(1+(d^2)/(D^2))^(-3//2)-(1+(4d^2)/(D^2))^(-3//2)]`
Applying binomial approximation `therefore" "dltltD`
`=(2KqD)/(D^3)[1-(3)/(2)(d^2)/(D^2)-(1-(3xx4d^2)/(2D^2))]" "," "=(2KqD)/(D^3)[(12)/(2)(d^2)/(D^2)-(3)/(2)(d^2)/(D^2)]=(9Kqd^2)/(D^4)`