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Potential Energy of a Dipole in Uniform Electric Field

When three el...

Question

When three electric dipoles are near each other, they each experience the electric field of the other two, and the three dipole system has a certain potential energy. Figure below shows three arrangements $(1), (2)$ and $(3)$ in which three electric dipoles are side by side. All three dipoles have the same magnitude of electric dipoles have the same magnitude of electric dipole moment, and the spacings between adjacent dipoles are identical. If $U_{1}$ , $U_{2}$ and $U_{3}$ are potential energies of the arrangements $(1), (2)$ and $(3)$ respectively then-

U_{1} > U_{2} > U_{3}

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U_{1} > U_{3} > U_{3}

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U_{1} > U_{2} = U_{3}

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U_{1} = U_{2} = U_{3}

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Solution

The correct option is C $U_{1} > U_{2} > U_{3}$
$U_{1}$ will be positive and greatest since all forces among dipoles are repulsive. $U_{2}$ is negative as potential energy of first and second dipole pair cancels out potential energy of interaction of first and third, that is negative. In $(c)$ effect of attraction is greatest.

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