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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.
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Solution
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`
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