Question

The dipole moment of a given system is:
A. $\sqrt 3 ql$ along a perpendicular bisector of the $q - q$ line.
B. $2\,ql$ along perpendicular bisector of $q - q$ line.
C. $ql\sqrt 2 $ along perpendicular bisector of $q - q$ line.
D. $0$

Answer 1

Hint: Here, we will use the formula of dipole moment to calculate the dipole moment of a given system. Here, a system of charges is taken as an equilateral triangle in which the charges are taken on the three corners of a triangle. Here, the angle at the charge $ - 2q$ is bisected perpendicularly.

Complete step by step answer:
When there is a separation of charges it will lead to a dipole moment. Also, we can say that the difference in the electronegativity between two chemically bonded charges leads to a dipole moment.
Now, the formula of the dipole moment is given by
$\mu = Q \times r$
Here, $\mu $ represents the dipole moment, $Q$ represents the charge in the system, and $r$ represents the distance of separation between the two charges.
Here, we can also represent the dipole moment between the charges as $P$ .
Now, in the question, we are given a system of charges, therefore, the dipole moment of the system of charges is given by
$\vec P = \sum {{q_i}} {\vec r_i}$
Now, if we consider a charge $ - 2q$ as $ - q - q$, therefore, dipoles on both sides are given by $q{l_{}}$ and $ - q{l_{}}$ .
Also, if we consider a perpendicular bisector of the charge $ - 2q$ , such that it divides the angle as $30^\circ - 30^\circ $ , hence, the perpendicular component of the dipole is $ - 2q\,\cos 30^\circ $ , therefore, the above equation becomes
$\vec P = \,q{l_{}} - q{l_{}} + 2q{l_{}}\cos 30^\circ $
$\vec P = 2q{l_{}} \times \dfrac{{\sqrt 3 }}{2}$
$\vec P = \sqrt 3 ql$
Hence, the dipole moment of a given system is $\sqrt 3 ql$ along the perpendicular bisector of the $q - q$ line.

So, the correct answer is “Option A”.

Note:
A bond dipole moment is used to measure the polarity of a chemical bond between two atoms in a molecule. It involves the concept of electric dipole moment that is the measure of the separation of negative and positive charges in a system. The bond dipole moment is different from the dipole moment of the whole molecule.