Question

The distance between \[{H^ + }\]and \[C{l^ - }\] ions in HCl molecules is \[1.38\mathop A\limits^0 \] . The potential due to this dipole at a distance of \[10\mathop A\limits^0 \]on the axis of dipole is
A. 2.1V
B. 1.8V
C. 0.2V
D. 1.2V

Answer 1

Hint:A dipole exists in any system when there is a separation of charge whether it is an ionic or covalent bond. An electric dipole moment can be calculated as the product of charge and the distance between them. Electric potential is defined as the amount of work required to displace a unit charge from a point to the desired point against an electric field.

Formula usedDipole moment is given as
\[p = q \times d\]
Where q is the charge and d is the distance of two charges.
The potential due to this dipole is given as
\[V = \dfrac{{p\cos \theta }}{{4\pi {\varepsilon _0}{r^2}}}\]
Where p is dipole moment, r is distance from dipole and k is coulomb’s constant,\[k = \dfrac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}N{m^2}\].

Complete step by step solution:
Given the distance between \[{H^ + }\]and \[C{l^ - }\]ions, \[d = 1.38\mathop A\limits^0 = 1.38 \times {10^{ - 10}}m\]
The potential due to the dipole at a distance, \[r = 10\mathop A\limits^0 = 10 \times {10^{ - 10}}m\]
As we know Charge, \[q = 1.6 \times {10^{ - 19}}C\]
As the potential due to this dipole on the axis, \[\theta = {0^0}\]
The potential due to this dipole is,
\[V = \dfrac{{p\cos \theta }}{{4\pi {\varepsilon _0}{r^2}}}\]
Here the dipole moment can be as \[p = q \times d\].
Now,
\[V = \dfrac{1}{{4\pi {\varepsilon _0}}} \times \dfrac{{qd\cos \theta }}{{{r^2}}} \\ \]
Substituting all the values, we get
\[\begin{array}{l}V = \dfrac{{9 \times {{10}^9} \times 1.6 \times {{10}^{ - 19}} \times 1.38 \times {{10}^{ - 10}}\cos {0^0}}}{{{{(10 \times {{10}^{ - 10}})}^2}}}\\ \therefore V {\rm{ = 0}}{\rm{.2V}}\end{array}\]
Therefore the potential due to the dipole on the axis of dipole is 0.2V.

Hence option C is the correct answer.

Note: An electric dipole consists of a pair of two charges equal in magnitude (q) but opposite in nature (i.e. one is a positive charge and the other is a negative charge). These two charges are separated by a distance of length d. Dipole moments are a vector quantity.