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Question

Two identical electric dipoles are arranged on x-axis as shown in figure. Electric field at the origin will be ( Assume 14πϵ0=K )

A
zero
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B
Kp2r3^j
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C
Kp2r3^j
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D
2Kpr3^ikpr3^j
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Solution

The correct option is C Kp2r3^j
The dipoles can be resolved along x and y axes as shown in figure.

The formulae for electric field at axial and equatorial points of a dipole are:
E(axial)=2Kpr3 along the dipole
E(equatorial)=Kpr3 opposite to the direction of dipole.
Electric field at centre due to horizontal components of dipoles will cancel out.
Total electric field at centre due to vertical components will be E=Kp/2r3×2 in vertically downward direction.
E=Kp2r3^j

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