Q12Q - Fundamentals Of Physics

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 22-31 shows two arrangements in which three electric dipoles are side by side. Each dipole has the same magnitude of electric dipole moment, and the spacing between adjacent dipoles is identical. In which arrangement is the potential energy of the three-dipole system greater?

Step-by-Step Solution

Answer

The arrangement in which the potential energy of the three-dipole system has greater value is (b).

 

Step 1: The given data

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.

 

Step 2: Understanding the concept of electric dipole

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,

 $\overrightarrow{U}=-\overrightarrow{p}.\overrightarrow{E}$                              (i)

 

Step 3: Calculation of the greater arrangement from the given dipole systems

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.