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Three identical dipoles with charges q and -q, and separation A between the charges, are placed at the corners of an equilateral triangle of side D as shown in (Fig. 3.123). Find the interaction energy of the system (a lt lt d). . |
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Answer» <P>  . Electric field `E_1` due to DIPOLE at `B` is `E_1 = (k 2 p cos 60^(@) )/(d^3)` and `E_2 = (k SIN 60^(@))/(d^3)` Potential energy between `A and B` is `- vec p . vec E = - vec p.(vec E_1 + vec E_2) = - vec p. vec E_1` , `(because vec p _|_ vec E_2)` or `-p E_1 cos 180^(@) = p E_1 = (k 2 p^2 cos 60^(@))/(d^3) = (q^2 a^2)/(4 pi epsilon_0 d^3)` Net energy of system is `3 q^2 a^2 // 4 pi epsilon_0 d^3`. |
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