Question

Derive an expression for the intensity of electric field at a point in broadside position or on [4)
an equatorial line of an electric dipole.

Answer 1

The electric field at a point, P due to an electric dipole.Due to the positive charge, the positive test charge will experience repulsive force whereas due to negative charge test charge will experience the attraction. Hence,

`|E_+| = 1/(4piin_0)  q/(r^2 + a^2)`

`|E_-| = 1/(4piin_0)  q/(r^2 + a^2)`

`E_R = E_+cos theta + E_-  cos theta`

`= 1/(4piin_o)  (2q)/(r^2 + a^2) . cos theta`

`= 1/(4piin_0) (2p)/(r^2 + a^2) . (q/(r^2 + a^2)^(1/2))`

`E_R = 1/()4piin_0 (2q xx a)/(r^2 + a^2)^(3/2) = 1/(4piin_0) p/(r^2 + a^2)^(3/2)`

if  r >>> a, then

`E_R = 1/(4piin_0) p/r^3`