91Ó°ÊÓ

a) Figure 22-31 represents three electric dipole experiencing potential energy as a three-dipole system.

b) Each dipole has same magnitude of electric dipole moment and spacing is identical.

An electric dipole is none other than two opposite charges placed at a certain distance from each other. The value of the potential energy of a given dipole is the negative of the dot product of the dipole moment and electric field. Now, for the given arrangements of the electric dipoles, we can check the repulsion among them. Thus, the more repulsion, the greatest; the more positive is the energy value.

The potential energy of the dipole system,

$\stackrel{→}{U}=−\stackrel{→}{p}.\stackrel{→}{E}$ (i)

For case a,

The energy will be greater but less in value in comparison to the second case due to one dipole being repulsive in nature and thus, the overall energy effect is attractive.

For case b,

From equation (i) and the given figure, we can say that the energy value for this case will be more positive and greater in repulsive ground as the forces involved are all repulsive.

Hence, the arrangement (b) is the greater energy case.