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Obtain the ratio of Electric field formed by an ideal dipole at points lying on axial and equatorial axis.
Asked by avaneesh1162 | 12 Jun, 2021, 11:06: AM
Let a dipole consists of charges +q and -q that are separated by a distance d is placed at origin of
X-Y coordinate system so that mid point of dipole coinicides with origin.

Electric field at a point x = r on x-axis is given as

..................................(1)

Where K = 1/ (4πεo ) is Coulomb's constant

if we consider dipole moment p = ( q × d )   and  r >> d/2 , then eqn.(1) is written as

Ex  = K × [ ( 2 p ) / r3  ]  ............................ (2)

Electric field at a point y = r on y-axis is given as

Ey = 2 E cosθ  .................................(3)

Where  E is given as
Hence we get Eas   ,   .........................(4)

In above expression , we used the approximation r >> d  and  dipole moment p = ( q × d )

From eqn.(2) and eqn.(4) , we get  ( Ex / Ey )  = 2
Answered by Thiyagarajan K | 12 Jun, 2021, 02:59: PM

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