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Which of the following unit conversions of dipole moments is correct?
(A) $1D = 3.3356Cm$
(B) $1D = 3.3356 \times {10^{ - 30}}Cm$
(C) $1Cm = 3.3356D$
(D) $1Cm = 3.3356 \times {10^{ - 30}}D$

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Last updated date: 13th Jun 2024
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Answer
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Hint: We are given with four unit conversion of the dipole moment and are asked to find out the correct one out of them. In other words, we are asked to evaluate the standard unit conversion of dipole moment. Thus, we will take into consideration the standard setup for a dipole and then calculate its dipole moment.

Complete Step By Step Solution:
In the standard setup,
The standard unit Debye is expressed in the electrostatic unit of charge.
That means,
$1D = {10^{ - 18}}esu.cm$
Now,
We know,
$1esu = 3.3356 \times {10^{ - 10}}C$
And
$1cm = {10^{ - 2}}m$
Putting in these values, we get
$1D = {10^{ - 18}} \times 3.356 \times {10^{ - 10}} \times {10^{ - 2}}Cm$
Further, we get
$1D = 3.3356 \times {10^{ - 30}}Cm$

Hence, the correct answer is (B).

Additional Information: In this question, we discussed the dipole moment. But what is the dipole moment and what is the dipole? We will discuss these two points in this briefing. Now, Dipole is nothing but a setup of two opposite charges of equal magnitudes placed at a fixed distance from each other. This setup is done to study the effect on a separate particle placed at the equatorial plane or the axial plane or at any random position in space. The dipole moment is a value assigned to a dipole setup so as to get an idea of the effectiveness of the dipole setup. The value of a dipole is calculated by the product of the magnitude of the either charge with the distance of separation of the charges. The distance of separation of the charges is also called the length or the size of the dipole.

Note: Here we have used the standard setup as the unit conversion is asked for a general case. If some other situation was asked, then the conversion would have been different.