On the x-y plane to point charges `+q` and `-q` are placed at positiions `(0,l)` and `(0,-l)` respectively. Find an expression for the intensity of electric field at a point `(0,y)` where `ygtl`. Under what condition does the charge system bechave as a dipole and hence express the electric field in terms of the dipole moment of the dipole so formed.

Explanation

Suppose, electric field intensity at the point C due to the charges A and B are `E_(1)` and `E_(2)`, respectively.
`:.E_(1)=1/(4 pi epsilon_(0)) .q/((y-l)^(2))`, along `vec(CY)`
`E_(2)=1/(4 pi epsilon_(0)) . q/((y+l)^(2))`, along `vec(CA)`

As `E_(1)` and `E_(2)` are acting the opposite directions and `E_(1)gtE_(2)`, the resultant electric field at C is
`E=E_(1)-E_(2)`
`=1/(4 pi epsilon_(0)) . q.((y-l)^(2)) - 1/(4 pi epsilon_(0)) . q/((y+l)^(2))`
`=q/( 4 pi epsilon_(0)) [ 1/((y-l)^(2)) - 1/ ((y+l)^(2))] = q/(4 pi epsilon_(0)) . (4yl)/((y^(2)-l^(2))^(2))`
`=1/(4 pi epsilon_(0)) . (4qyl)/(y^(4)) [ :' y gtl]`
`=1/(4pi epsilon_(0)) . (4ql)/(y^(3))`, along `vec(CY)`
If the value of l is small, the combination of the charges behave as an electric dipole with dipole moment, `p=qxx2l`.
In that case `E=1/(4 pi epsilon_(0)) . (2p)/(y^(3))`, along `vec(CY)`