Four configurations of two ideal electric dipoles are shown in List-I. Each dipole has magnitude p and the dipoles are 2r apart along x. X is the midpoint. Match each configuration with the resultant electric field at X.
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Question

Four configurations of two ideal electric dipoles are shown in List-I. Each dipole has magnitude p and the dipoles are 2r apart along x. X is the midpoint. Match each configuration with the resultant electric field at X.

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G1 Physics · Accepted Answer

At the midpoint, each dipole is at distance r.

Equatorial field magnitude = p/(4πε₀r³), opposite to p. Axial field magnitude = 2p/(4πε₀r³), along p.

P: two +ĵ dipoles give E = −pĵ/(2πε₀r³) → 2. Q: equal and opposite transverse dipoles cancel → 1. R: one transverse +ĵ dipole and one axial +î dipole give p(2î−ĵ)/(4πε₀r³) → 4. S: two axial +î dipoles give pî/(πε₀r³) → 5.

Thus P→2, Q→1, R→4, S→5, i.e. option C.