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Electric Field due to Dipole

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The electric field due to a dipole at a distance on its axis is

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Starting from Eq. 24-54 derive the expression for the electric field due to a dipole at a point on the dipole axis.

The locus of the points (in the xy -plane) where the electric field due to a dipole (dipole axis is along x -axis and its equatorial is along y -axis) is perpendicular to its axis, is

Find the locus of points where the electric field due to a dipole is (i) perpendicular to its axis , (ii) anti-parallel to the axis . [Hint : "tan" alpha = ("tan"theta)/(2) ]

Electric Field Due to Electric Dipoles || Potential Due to Dipole || Examples on Dipoles

Electric field due to an electric dipole is