Question

There are two dipoles in space with dipole moment $\overrightarrow{P_1}=\hat{i}+2\hat{j}+\hat{k}$ $and$ $\overrightarrow{P_2}=2\hat{i}-3\hat{j}+\hat{k}$. What is the net dipole moment of the arrangement?

• A. $-\hat{i}+5\hat{j}$
• B. $3\hat{i}-j+2\hat{k}$
• C. $\hat{i}-5\hat{j}$
• D. $\frac{3\hat{i}-\hat{j}+2\hat{k}}{\sqrt{14}}$

Answer 1

The correct option is B $3\hat{i}-j+2\hat{k}$

Since dipole moment is a vector quantity, to find the net dipole moment of the arrangement are can add these using vector algebra.
Given $\overrightarrow{P_1}=\hat{i}+2\hat{j}+\hat{k}$ $and$ $\overrightarrow{P_2}=2\hat{i}-3\hat{j}+\hat{k}$
$Sonet$ $\overrightarrow{p}=\overrightarrow{P_1}+\overrightarrow{P_2}=(\hat{i}+2\hat{j}+\hat{k})+(2\hat{i}-3\hat{j}+\hat{k})$
$=3\hat{i}-j+2\hat{k}$