Question

Two charges of magnitude -4C and 4C are placed at points (1, 2, 3) and (3, 4, 2) respectively. What is the dipole moment?

• A. $2\hat{i}-2\hat{j}-\hat{k}Cm$
• B. $-8\hat{i}+8\hat{j}+4\hat{k}Cm$
• C. $8\hat{i}+8\hat{j}-4\hat{k}Cm$
• D. $12cm$

Answer 1

The correct option is C $8\hat{i}+8\hat{j}-4\hat{k}Cm$

The dipole moment will be in the direction of the vector connecting -4C to 4C i.e., from (1, 2, 3) to (3, 4, 2).
Let $\overrightarrow{L}\to$ which is a vector representing the distance between -4C charge to +4C Charge
$\overrightarrow{L}$ = Portion vector of +4C charge – Position vector of -4C charge.

$\overrightarrow{L}$ = $(3\hat{i}+4\hat{j}+2\hat{k})-(1\hat{i}+2\hat{j}+3\hat{k})$
$=2\hat{i}+2\hat{j}-\hat{k}$
Now $\overrightarrow{p}$ = $q\overrightarrow{L}=4\times (2\hat{i}+2\hat{j}-k)$
$=8\hat{i}+8\hat{j}-4\hat{k}$